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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+111x^70+4x^71+262x^72+44x^73+400x^74+108x^75+408x^76+204x^77+424x^78+292x^79+451x^80+228x^81+361x^82+100x^83+263x^84+36x^85+160x^86+8x^87+102x^88+63x^90+37x^92+13x^94+11x^96+4x^98+1x^120

The gray image is a linear code over GF(2) with n=316, k=12 and d=140.
This code was found by Heurico 1.16 in 1.83 seconds.