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  X  X  1  0  X  1  0  1  1 X^2  0  0 X^2  1  1  0  1  1 X^2  X  0  X  X  0  1  X  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  X  X  0 X^2  0  X X^2+X  X X^2  0 X^2+X  0 X^2+X  X  X X^2 X^2  0  0 X^2  X X^2  0  0  0  X  X  X  0 X^2  0 X^2  X  X  X X^2+X  0 X^2  X X^2  0
 0  0  X  0  X  X X^2+X  0  0  0  X  X  X  0 X^2 X^2+X X^2 X^2  0 X^2+X  0  X  X X^2+X X^2  0  X X^2+X  X  0  0 X^2+X X^2 X^2+X X^2+X  X  X  0 X^2+X X^2+X X^2+X X^2+X X^2  X X^2  X X^2 X^2+X X^2+X  X  X X^2+X X^2+X  0
 0  0  0  X  X  0 X^2+X  X X^2  X X^2  0  X X^2 X^2+X  X  0  X X^2+X  X X^2 X^2+X  0  0  0 X^2  X  0  0 X^2+X  X  0 X^2+X  X  X X^2+X X^2+X  X X^2+X X^2+X X^2+X X^2+X  X X^2+X  X X^2+X  X  X  0 X^2+X X^2 X^2+X X^2+X  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2 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+50x^44+92x^45+145x^46+234x^47+298x^48+342x^49+461x^50+578x^51+687x^52+790x^53+830x^54+828x^55+707x^56+624x^57+465x^58+316x^59+234x^60+156x^61+127x^62+90x^63+57x^64+42x^65+17x^66+2x^67+13x^68+2x^69+2x^70+1x^72+1x^74

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 4.44 seconds.