The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+88x^81+96x^82+170x^83+119x^84+204x^85+137x^86+186x^87+93x^88+180x^89+130x^90+214x^91+99x^92+148x^93+67x^94+62x^95+1x^96+20x^97+11x^98+8x^99+5x^100+3x^102+1x^104+2x^106+1x^108+1x^114+1x^126

The gray image is a linear code over GF(2) with n=352, k=11 and d=162.
This code was found by Heurico 1.16 in 0.919 seconds.