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

generates a code of length 54 over Z2[X]/(X^3) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+49x^44+86x^45+139x^46+246x^47+284x^48+350x^49+463x^50+552x^51+691x^52+860x^53+876x^54+752x^55+705x^56+616x^57+452x^58+328x^59+218x^60+166x^61+124x^62+98x^63+58x^64+34x^65+17x^66+8x^67+10x^68+8x^70+1x^78

The gray image is a linear code over GF(2) with n=216, k=13 and d=88.
This code was found by Heurico 1.16 in 4.22 seconds.