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

generates a code of length 73 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+124x^64+4x^65+208x^66+40x^67+310x^68+128x^69+416x^70+216x^71+549x^72+248x^73+500x^74+216x^75+441x^76+128x^77+170x^78+40x^79+137x^80+4x^81+98x^82+77x^84+14x^86+21x^88+2x^90+3x^92+1x^116

The gray image is a linear code over GF(2) with n=292, k=12 and d=128.
This code was found by Heurico 1.16 in 1.76 seconds.