The generator matrix

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

generates a code of length 80 over Z2[X]/(X^3) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+56x^73+87x^74+202x^75+135x^76+176x^77+108x^78+208x^79+131x^80+236x^81+121x^82+152x^83+97x^84+168x^85+57x^86+72x^87+11x^88+4x^89+6x^90+6x^91+6x^92+2x^94+1x^98+1x^100+1x^102+1x^104+1x^106+1x^108

The gray image is a linear code over GF(2) with n=320, k=11 and d=146.
This code was found by Heurico 1.16 in 0.73 seconds.