The generator matrix

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

generates a code of length 41 over Z2[X]/(X^3) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+89x^28+63x^30+8x^31+187x^32+88x^33+270x^34+200x^35+807x^36+480x^37+1757x^38+816x^39+2972x^40+912x^41+2977x^42+816x^43+1767x^44+480x^45+795x^46+200x^47+256x^48+88x^49+197x^50+8x^51+57x^52+71x^54+8x^56+11x^58+2x^62+1x^66

The gray image is a linear code over GF(2) with n=164, k=14 and d=56.
This code was found by Heurico 1.16 in 9.89 seconds.