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

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+148x^70+4x^71+234x^72+32x^73+336x^74+112x^75+400x^76+224x^77+440x^78+280x^79+526x^80+224x^81+398x^82+112x^83+215x^84+32x^85+146x^86+4x^87+112x^88+47x^90+39x^92+18x^94+7x^96+2x^98+1x^100+1x^106+1x^124

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 4.29 seconds.