The generator matrix

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

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+174x^75+209x^76+316x^77+208x^78+196x^79+187x^80+162x^81+115x^82+104x^83+72x^84+64x^85+44x^86+58x^87+37x^88+50x^89+15x^90+10x^91+5x^92+16x^93+2x^94+1x^96+2x^103

The gray image is a linear code over GF(2) with n=320, k=11 and d=150.
This code was found by Heurico 1.11 in 0.5 seconds.