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

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+106x^89+23x^90+16x^91+24x^92+56x^93+8x^94+6x^96+12x^97+2x^105+1x^106+1x^112

The gray image is a linear code over GF(2) with n=364, k=8 and d=178.
This code was found by Heurico 1.16 in 63.1 seconds.