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

generates a code of length 97 over Z2[X]/(X^3) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+54x^89+89x^90+80x^91+103x^92+100x^93+171x^94+186x^95+177x^96+242x^97+194x^98+170x^99+124x^100+78x^101+69x^102+40x^103+22x^104+20x^105+37x^106+28x^107+13x^108+14x^109+15x^110+6x^111+8x^112+4x^113+2x^115+1x^166

The gray image is a linear code over GF(2) with n=388, k=11 and d=178.
This code was found by Heurico 1.16 in 35 seconds.