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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+211x^70+352x^72+40x^73+522x^74+152x^75+770x^76+344x^77+868x^78+440x^79+940x^80+600x^81+843x^82+264x^83+604x^84+168x^85+385x^86+40x^87+286x^88+174x^90+103x^92+64x^94+13x^96+5x^98+2x^100+1x^124

The gray image is a linear code over GF(2) with n=320, k=13 and d=140.
This code was found by Heurico 1.16 in 26.6 seconds.