The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  1  X  1 X^2+X  1 X^2+X  1  0  1 X^2+X  1  X X^2  X  1  1  1  1  1  1 X^2 X^2  0  1  X  X  1  1  1  1  X  1  1 X^2  1  1  1  0  1  1  X  1  1  0  1  1  1  1  1 X^2+X  X X^2+X  0  0  1  1  X  1  0  X  1 X^2+X  0  X  X  1 X^2+X  1 X^2+X  1  1  1  1  1  1  0  1  X
 0  1  0  0  1  1  1 X^2  1  1 X+1 X^2+X  X  1 X^2+X  1 X^2+X+1 X^2+X X+1  1 X^2  1  1 X^2+X X^2+X X^2+X X^2+1 X+1 X^2+X X^2+1  1  1  X  0  1 X^2  0 X+1 X^2+X+1 X+1  1  0 X^2+1  1 X^2+X X+1 X^2+X+1  1  X X+1  1 X^2+1 X^2+X+1  X X^2  0  0 X^2+1 X^2  1 X^2+X  1 X^2  1 X^2+X X^2+X+1  1 X^2+X+1  1  X X^2  1  1  1  X X^2+X X^2  X  1 X^2+1  0 X+1  0  X  1  X  1  1
 0  0  1 X+1 X^2+X+1  0 X+1  X  1  X  0  1  1  1  X X^2 X^2+X  1 X^2+1 X+1 X^2+1  X  1  1 X+1  0  0 X^2+X+1 X^2+1  X  1 X^2  1 X^2 X^2+X+1  1 X^2+X X^2+X+1 X^2+1 X^2+X X^2+X X^2+X+1 X+1 X+1 X^2+1 X^2+X+1 X^2  X  0  X  1  0 X^2+X+1  1  X X^2+X  1 X^2+1 X^2 X^2+X+1  1 X^2+X+1  1 X+1  X  X  X X^2+1  X  1  1  X X^2+1 X^2  1 X^2  1 X^2+X+1 X^2+1  1 X^2+X+1 X^2+X X+1 X+1 X^2+X+1  1 X^2+X+1  1
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  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  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 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  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 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  0 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2  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+160x^80+244x^81+440x^82+624x^83+670x^84+636x^85+602x^86+668x^87+657x^88+612x^89+526x^90+540x^91+374x^92+388x^93+322x^94+180x^95+180x^96+152x^97+70x^98+36x^99+56x^100+16x^101+20x^102+9x^104+4x^106+4x^108+1x^112

The gray image is a linear code over GF(2) with n=352, k=13 and d=160.
This code was found by Heurico 1.16 in 5.44 seconds.