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  0  X  X  X X^2  X  X  X  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0 X^2  X  X X^2+X  0 X^2+X X^2+X  0  X  X X^2+X X^2  0  X X^2+X  X X^2  X X^2 X^2+X X^2  X X^2+X X^2+X X^2+X X^2+X X^2+X  X X^2 X^2+X X^2  X X^2 X^2+X  X  X  X  X X^2 X^2+X  X X^2+X X^2 X^2+X
 0  0  X  0  0  0  0  0  0  0 X^2+X X^2  X  X  X  X  0  X  0 X^2+X X^2+X  X X^2+X  X X^2 X^2+X  X X^2 X^2 X^2+X  0  0  0 X^2 X^2+X  X X^2  X X^2+X X^2  X X^2 X^2+X  0 X^2+X  0  X X^2 X^2+X  X  0  X X^2  0
 0  0  0  X  0  0  0  X X^2+X  X  X X^2+X  0  X X^2  0 X^2+X X^2+X X^2+X X^2 X^2+X  0 X^2 X^2  0  X  0 X^2  0  X  X X^2+X  X X^2  0  X  0 X^2+X X^2+X X^2+X  0 X^2+X X^2+X X^2+X X^2+X X^2  0 X^2+X  X  X  0  0 X^2 X^2+X
 0  0  0  0  X  0  X  X  X X^2  X  X  X X^2 X^2 X^2+X X^2+X X^2 X^2  0 X^2+X X^2+X  X  0 X^2 X^2 X^2+X X^2  X X^2+X  0  0 X^2 X^2+X  0  X X^2 X^2  X  X  X X^2+X X^2+X  0 X^2+X X^2 X^2+X  X  0  0  X X^2+X  X  0
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  X  X X^2+X  0  X X^2 X^2 X^2 X^2+X X^2 X^2+X  0 X^2+X X^2+X X^2+X X^2+X  0 X^2 X^2 X^2  X  0 X^2  X X^2  0 X^2+X X^2  X  X X^2+X X^2+X X^2+X  X X^2 X^2+X  X  X X^2+X  X X^2+X  X X^2  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2  0  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+237x^44+550x^46+831x^48+80x^49+1088x^50+528x^51+2087x^52+1440x^53+2704x^54+1440x^55+2120x^56+528x^57+1146x^58+80x^59+768x^60+448x^62+216x^64+78x^66+11x^68+2x^70+1x^92

The gray image is a linear code over GF(2) with n=216, k=14 and d=88.
This code was found by Heurico 1.16 in 16.1 seconds.