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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+46x^80+88x^81+56x^82+138x^83+95x^84+138x^85+197x^86+220x^87+255x^88+158x^89+199x^90+94x^91+81x^92+82x^93+37x^94+24x^95+20x^96+34x^97+21x^98+22x^99+11x^100+12x^101+2x^102+12x^103+2x^104+2x^107+1x^148

The gray image is a linear code over GF(2) with n=352, k=11 and d=160.
This code was found by Heurico 1.16 in 0.942 seconds.