The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 X X 2 X X X X X 0 X 0 X X X X 1 1 1 2 2 0 X 1 X 1 1 1 X 1 1 1 2 X 1 1 X X 2 X 1
0 X 0 0 0 0 0 0 0 0 2 X X X+2 0 X+2 X+2 0 2 X X+2 2 X X X 2 X 0 X 2 X+2 X X+2 X+2 X+2 X+2 X 2 X+2 X+2 0 2 X X+2 X 0 X+2 2 X X+2 X X 2 X+2 2 X 2 2 X X 0 X X+2 X+2 X 2 2 X X 2 X 0 X 2 2 2 X 2 0 X 2 X+2 2 X+2 X X X X+2 2
0 0 X 0 0 0 0 0 0 0 X+2 2 X X X X 0 X X 0 X+2 2 0 X+2 X X X+2 X+2 2 0 X+2 0 2 X+2 X 0 2 2 2 0 X X X+2 X+2 X X 2 X 2 X 2 0 0 0 2 X X+2 2 X X X X+2 2 0 2 0 X+2 2 X X 2 2 0 X+2 X X+2 0 X 2 2 2 X X X+2 X X+2 2 X 0
0 0 0 X 0 0 0 X X+2 X X X+2 0 X 2 0 X+2 X+2 2 X+2 X+2 X 0 2 0 2 X X X 2 X 0 X+2 0 X X+2 0 2 2 X X X+2 0 2 X 0 2 X+2 X+2 0 2 2 X 2 2 X+2 2 0 X X X 2 2 2 2 X+2 X+2 X+2 X 0 X+2 X+2 X+2 X X+2 2 X X+2 X X+2 X 2 X X+2 X X+2 0 0 0
0 0 0 0 X 0 X X X 2 X X X 2 2 X+2 X+2 2 X+2 2 X+2 X X+2 2 2 X 0 X+2 2 X+2 X+2 X X+2 X 0 X+2 X+2 0 X 2 0 2 0 X+2 2 2 2 0 X X X+2 X+2 0 X+2 X+2 X+2 X+2 X 0 X 2 2 X+2 0 2 2 X 0 0 0 0 X 2 0 2 0 X+2 2 X+2 2 X+2 X X+2 X+2 X+2 0 0 2 0
0 0 0 0 0 X X 2 X+2 X+2 X X X+2 0 X 2 2 2 X X+2 0 2 2 0 X 0 X 2 2 X+2 X+2 X+2 X+2 0 2 2 2 2 X+2 0 0 X+2 X+2 X+2 X X X+2 X+2 2 2 2 0 0 X X+2 0 X 0 0 0 X+2 2 X+2 0 X+2 X X+2 X+2 X 2 X+2 X 0 X X+2 2 X+2 0 X X X 2 0 X X X 2 X+2 X+2
0 0 0 0 0 0 2 2 2 2 2 2 2 0 2 0 0 0 2 2 0 0 0 0 2 2 0 2 2 0 0 0 0 2 2 2 2 2 2 0 2 0 0 0 2 0 2 2 2 2 0 2 0 0 0 0 0 0 2 2 2 2 2 0 0 0 0 2 2 0 0 2 0 0 2 0 2 2 0 2 0 0 0 0 0 0 2 0 2
generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.
Homogenous weight enumerator: w(x)=1x^0+30x^76+118x^77+194x^78+254x^79+341x^80+422x^81+527x^82+656x^83+771x^84+836x^85+1057x^86+1240x^87+1157x^88+1248x^89+1286x^90+1234x^91+1115x^92+858x^93+685x^94+544x^95+447x^96+356x^97+258x^98+214x^99+188x^100+94x^101+68x^102+66x^103+40x^104+30x^105+20x^106+16x^107+4x^108+6x^109+2x^112+1x^122
The gray image is a code over GF(2) with n=356, k=14 and d=152.
This code was found by Heurico 1.16 in 30.7 seconds.