The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+216x^75+197x^76+292x^77+178x^78+220x^79+143x^80+210x^81+83x^82+114x^83+75x^84+92x^85+38x^86+72x^87+19x^88+34x^89+20x^90+18x^91+12x^92+12x^93+1x^96+1x^98

The gray image is a linear code over GF(2) with n=320, k=11 and d=150.
This code was found by Heurico 1.16 in 8.27 seconds.