The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+230x^83+114x^84+390x^85+114x^86+306x^87+141x^88+216x^89+24x^90+148x^91+68x^92+94x^93+18x^94+34x^95+16x^96+52x^97+4x^98+42x^99+9x^100+16x^101+8x^103+1x^108+2x^112

The gray image is a linear code over GF(2) with n=352, k=11 and d=166.
This code was found by Heurico 1.16 in 2.04 seconds.