The generator matrix

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

generates a code of length 74 over Z2[X]/(X^3) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+134x^67+189x^68+316x^69+182x^70+442x^71+328x^72+422x^73+225x^74+422x^75+284x^76+424x^77+141x^78+248x^79+123x^80+100x^81+19x^82+14x^83+18x^84+12x^85+5x^86+14x^87+16x^88+6x^89+2x^90+6x^91+2x^98+1x^100

The gray image is a linear code over GF(2) with n=296, k=12 and d=134.
This code was found by Heurico 1.16 in 22.3 seconds.