The generator matrix

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

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+23x^84+176x^85+23x^86+30x^88+138x^89+30x^90+7x^92+60x^93+7x^94+3x^96+10x^97+3x^98+1x^130

The gray image is a linear code over GF(2) with n=352, k=9 and d=168.
This code was found by Heurico 1.16 in 0.394 seconds.