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

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+255x^44+8x^45+498x^46+8x^47+900x^48+168x^49+1316x^50+568x^51+2002x^52+1256x^53+2384x^54+1336x^55+2028x^56+600x^57+1332x^58+136x^59+825x^60+16x^61+422x^62+235x^64+56x^66+21x^68+8x^70+4x^72+1x^84

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 21.8 seconds.