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  X  X  0  X X^2  0  X  X  0  X  X  X  0 X^2  X X^2  0  X  X X^2  0  X  0 X^2  0 X^2  X  X X^2 X^2  X  X X^2  1  1  1  1  1  1  0  1  1
 0  X  0  X  0  0 X^2+X X^2+X  0  0  X  X  0  0 X^2+X X^2+X X^2 X^2  X X^2+X X^2 X^2 X^2+X  X X^2 X^2  X X^2+X X^2 X^2 X^2+X  X X^2  X  X X^2+X  X  0  0  X  X  X X^2+X X^2  0 X^2  0  X  X  X  X X^2  X X^2+X  X  X  X  X  X X^2+X  X  X X^2+X X^2+X  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2
 0  0  X  X  0 X^2+X X^2+X  0 X^2 X^2+X X^2+X X^2 X^2  X  X X^2 X^2  X  X  0 X^2  X X^2+X X^2  0 X^2+X X^2+X X^2  0 X^2+X  X  0  X  X X^2  0  X  X X^2+X X^2 X^2+X X^2+X  0  X  X  X X^2+X  X X^2+X  X X^2+X  X  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  X X^2+X  0 X^2+X  X
 0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+100x^72+104x^74+28x^76+8x^78+4x^80+10x^88+1x^96

The gray image is a linear code over GF(2) with n=296, k=8 and d=144.
This code was found by Heurico 1.16 in 0.255 seconds.