The generator matrix

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

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+126x^74+116x^75+230x^76+192x^77+254x^78+100x^79+222x^80+128x^81+154x^82+92x^83+127x^84+80x^85+82x^86+44x^87+34x^88+16x^89+13x^90+12x^92+10x^94+9x^96+1x^98+4x^100+1x^108

The gray image is a linear code over GF(2) with n=320, k=11 and d=148.
This code was found by Heurico 1.16 in 0.601 seconds.