The generator matrix

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

generates a code of length 88 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+50x^86+96x^87+42x^88+10x^90+32x^91+12x^92+2x^94+9x^96+2x^106

The gray image is a linear code over GF(2) with n=352, k=8 and d=172.
This code was found by Heurico 1.16 in 0.372 seconds.