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

generates a code of length 89 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+72x^80+54x^82+4x^83+217x^84+92x^85+56x^86+276x^87+211x^88+332x^89+36x^90+204x^91+111x^92+84x^93+56x^94+28x^95+93x^96+4x^97+54x^98+53x^100+7x^104+2x^108+1x^156

The gray image is a linear code over GF(2) with n=356, k=11 and d=160.
This code was found by Heurico 1.16 in 1.03 seconds.