The generator matrix
1 0 0 1 1 1 1 1 0 1 1 1 2X 1 1 1
0 1 0 1 0 2 1 2 1 0 2X+1 2X+2 1 2 0 0
0 0 1 2 1 2 1 0 2 2 2X 2X+1 2X+1 2 0 0
0 0 0 2X 0 0 0 0 X X X X X 0 0 0
0 0 0 0 2X 0 0 X 2X 0 X X 0 2X 0 0
0 0 0 0 0 X 0 2X 2X X X 2X X 2X 0 0
0 0 0 0 0 0 X 2X 2X 0 0 X 2X X X 0
generates a code of length 16 over Z3[X]/(X^2) who´s minimum homogenous weight is 18.
Homogenous weight enumerator: w(x)=1x^0+44x^18+54x^20+190x^21+54x^22+432x^23+732x^24+540x^25+1404x^26+3410x^27+2160x^28+2592x^29+9180x^30+4320x^31+3456x^32+12018x^33+4320x^34+3456x^35+6426x^36+1728x^37+1728x^38+618x^39+156x^42+28x^45+2x^48
The gray image is a linear code over GF(3) with n=48, k=10 and d=18.
This code was found by Heurico 1.16 in 2.98 seconds.