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 X 0 X 0 X X^2 X X^2 X X 1 1 1 1 1 1 1 1 X X 0 0 X X X^2 X^2 X X X X X^2 X^2 0 0 1 1 1 1 X^2 0 1 X 1 1 1 X 1 1 1
0 X 0 X^2+X X^2 X^2+X X^2 X 0 X^2+X 0 X^2+X X^2 X X^2 X 0 X^2+X 0 X^2+X X^2 X X^2 X X^2+X X X^2+X X X X X X 0 X^2 0 X^2+X 0 X X^2 X^2+X X^2 X X^2+X X^2+X X X X X X X 0 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2+X X X^2 X^2 0 X^2 X^2+X X X^2 0 0 X^2+X 0
0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 0 X^2 X^2 0 X^2 0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2 X^2 0 X^2 0 X^2 X^2 0 0 X^2 X^2 X^2 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 X^2
generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.
Homogenous weight enumerator: w(x)=1x^0+34x^73+7x^74+12x^75+7x^76+2x^77+1x^86
The gray image is a linear code over GF(2) with n=292, k=6 and d=146.
This code was found by Heurico 1.16 in 0.236 seconds.