The generator matrix

 1  0  0  0  0  1  1  1  0  1 X^2  1  1 X^2+X  0  X  X  1  0  1  1 X^2  1  X  1  1 X^2  1  1  1  0 X^2+X  1  1  1  1  1  1 X^2+X  1  X  1  1  1  X  1  X X^2  1  1  1 X^2  0 X^2+X
 0  1  0  0  0  0 X+1  X X^2 X+1  1 X^2  1  1  1  1  1 X^2+1  1 X^2+X+1 X^2+1 X^2+X  1  X X^2+1  X  1  X  0  X  X  1 X^2+X+1 X^2+1  1 X^2  0  X X^2 X^2  1 X^2+X  X X^2  1 X^2+X+1  1  1 X^2+X+1 X+1 X^2  1  0  1
 0  0  1  0  0  0  1 X+1  1 X^2+1 X^2 X^2+1  1 X+1 X^2+X X^2+1 X^2+X  0  1 X^2  X  1 X^2+X  0  1  0  1 X^2+X+1 X^2  1  1 X^2+1 X^2+1  X  1 X+1  X X^2 X^2 X^2 X^2+X X^2+1  X X^2+1  1  0  0 X+1 X^2+X X^2+X X^2+X X^2+X+1  1 X^2+X+1
 0  0  0  1  0  1 X^2 X^2+1  1 X+1 X^2+1 X^2+X  X X^2+X+1  X X^2+X X+1  0 X^2 X^2+X+1 X^2+X+1  1  X  1 X^2+X+1 X^2 X+1  X X^2+1 X^2+1  0  0 X^2+1 X+1 X^2 X^2+X  X X+1  X X+1 X+1 X+1  X X^2+1  1  0 X+1  1 X^2+1  0 X+1 X^2+X+1 X^2+X+1 X^2
 0  0  0  0  1  1 X^2+1  X X+1 X^2+1 X^2+X X^2+1  0  0 X^2+1  1 X^2+X+1 X^2+X  X  0 X^2+1  X X+1 X^2+1  0 X^2+1 X+1 X^2 X^2 X^2+X+1 X+1  1  0 X^2 X^2  0  1 X+1  1  X X^2+X  1 X^2 X^2+X X^2+X X+1  1 X^2+X+1 X+1 X^2+X  1  X X^2 X+1
 0  0  0  0  0  X  0  X  X X^2+X  X X^2 X^2 X^2+X X^2 X^2 X^2+X  0  0 X^2+X X^2+X  X  0 X^2+X  X X^2  X  0 X^2+X X^2+X X^2+X  X X^2  0 X^2+X  X X^2+X  0  X  0  0 X^2  X  0 X^2  X  X  0 X^2  X  X X^2 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+245x^44+882x^45+1448x^46+2642x^47+4025x^48+5888x^49+7716x^50+9766x^51+12220x^52+12998x^53+14160x^54+14156x^55+12232x^56+10320x^57+8150x^58+5688x^59+3647x^60+2314x^61+1282x^62+682x^63+318x^64+168x^65+70x^66+26x^67+16x^68+6x^69+6x^70

The gray image is a linear code over GF(2) with n=216, k=17 and d=88.
This code was found by Heurico 1.13 in 162 seconds.