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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+32x^74+56x^75+57x^76+84x^77+105x^78+132x^79+137x^80+120x^81+94x^82+66x^83+50x^84+28x^85+21x^86+16x^87+8x^88+8x^89+4x^90+2x^91+2x^92+1x^148

The gray image is a linear code over GF(2) with n=320, k=10 and d=148.
This code was found by Heurico 1.16 in 0.436 seconds.