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

generates a code of length 86 over Z2[X]/(X^3) who´s minimum homogenous weight is 91.

Homogenous weight enumerator: w(x)=1x^0+8x^91+5x^92+2x^94

The gray image is a linear code over GF(2) with n=344, k=4 and d=182.
This code was found by Heurico 1.16 in 0.334 seconds.