The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+128x^84+144x^85+214x^86+112x^87+106x^88+48x^89+54x^90+24x^91+50x^92+24x^93+38x^94+16x^95+27x^96+4x^97+6x^98+4x^99+11x^100+4x^101+4x^103+4x^104+1x^108

The gray image is a linear code over GF(2) with n=352, k=10 and d=168.
This code was found by Heurico 1.16 in 0.43 seconds.