The generator matrix

 1  0  1  1  1 X^2  1  1  X  1  1 X^2+X  1  1 X^2  1  1  0  1  1  X  1  1  X  1  X  1  1 X^2  1  0  1  1  1 X^2+X  1  1 X^2+X  1 X^2  1 X^2  1  X  1  1  X  1  1  0  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  X  X  1  1  0  1  1 X^2+X X^2+X X^2+X  1  1  1  0  1  X  X  1 X^2+X  1 X^2
 0  1  1  0 X+1  1 X^2+X+1  0  1  0 X^2+1  1  0 X^2+X+1  1  0 X+1  1  0 X^2+1  1  0 X^2+1  1 X^2+X+1  1 X^2+X X^2+X  1  1  1  X X+1  X  1  1 X^2+X  1 X^2+X  1 X^2+X  1 X^2+X  1 X^2+X+1  1  0 X^2+X+1  1 X^2 X^2+X+1  1 X+1 X^2+1 X^2+X+1  1 X^2+1 X^2 X+1  1 X^2+X+1 X^2+X+1  1 X+1 X^2+1 X^2+X+1 X+1  X  1 X^2+1 X^2  1 X^2  1  1  1  1  1 X^2  X  1  0 X^2+X  1 X^2+X+1  1 X^2+X X^2
 0  0  X  0  0  0  0  X  X  X  X  X X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X  X  0  X  0 X^2+X X^2  X  X X^2  0  0  X X^2+X X^2 X^2 X^2+X X^2+X  X X^2 X^2  0 X^2+X X^2+X  0  X  X X^2+X  0  X X^2 X^2+X  0  0  X X^2+X X^2  X  X  0  X X^2 X^2+X X^2  0  X X^2+X  0  0  X X^2+X  X X^2 X^2  0 X^2+X X^2 X^2  X  0 X^2+X X^2 X^2+X  X  X
 0  0  0  X X^2 X^2+X X^2+X  X X^2 X^2 X^2+X  X X^2  0 X^2 X^2+X  X  X X^2+X X^2 X^2+X  0  X  0  0  X  X  0 X^2  X  X  0  0 X^2+X  0 X^2+X X^2 X^2  X X^2+X X^2+X  0 X^2 X^2+X X^2  X  X  X X^2  X X^2 X^2+X  X  0 X^2+X X^2  0 X^2+X  X X^2 X^2+X X^2  X  0 X^2+X  0 X^2+X X^2  X  0  X X^2+X X^2  0 X^2  0  X  0  X X^2+X  0 X^2+X  X  X X^2 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+247x^84+222x^86+205x^88+150x^90+108x^92+42x^94+33x^96+2x^98+8x^100+2x^108+3x^116+1x^120

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 1.08 seconds.