The generator matrix

 1  0  0  0  0  0  0  0  1  1  1  X  1  1  X  1  X  1  1  1  1  X  0  X  X  1  1  0  0  X  1  X  0  X  0  1  0  1  1  0  X  1  X  X  X  1  X  X  0  1  1  1  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  1  1  1  X X+1 X+1  X  X  1  1  1 X+1  1  X  0  X X+1  1  1  1  1  0  1  0  1  X  X  X  X  1  X X+1  0  X  1 X+1  0  X  X  0
 0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  1 X+1  1 X+1  1 X+1 X+1  1  1  1  1 X+1  1 X+1  1  1 X+1 X+1  X  X  1  0
 0  0  0  1  0  0  0  0  0  1  X  1  0 X+1  1  0 X+1 X+1  X  1 X+1  1  1  1  0  0 X+1  X  1  1  X  1  0  X X+1  0  1 X+1 X+1  0  0  0  X  1  0 X+1 X+1  1 X+1  X  X  0  1  0
 0  0  0  0  1  0  0  0  1  0  1  1  X  0  0  X X+1  1 X+1  0 X+1  0  1  X  1  1  X  0 X+1 X+1  0  1  X  0  1  0  1 X+1  X X+1  X  X  0  0 X+1  X  X  X X+1  1  X  X  1  0
 0  0  0  0  0  1  0  0  1  X  0 X+1  1 X+1  1 X+1 X+1  1  X  0  0  0  0  1  1 X+1  0  1  X  X  1  1  1  1  1 X+1  X  0 X+1  0 X+1 X+1  0  0  1  1 X+1  0  X  X  X X+1  0 X+1
 0  0  0  0  0  0  1  0  1 X+1 X+1  1 X+1  X  1  X  0  0  0 X+1  0 X+1 X+1 X+1  0  0  0  1  X  X  1 X+1  X X+1  1  X  0  1 X+1  1  1 X+1  0  X  1  0 X+1  0  1 X+1  1  1 X+1  X
 0  0  0  0  0  0  0  1  X  X  1  1  1 X+1 X+1  0 X+1  X X+1 X+1  1  1  X  0  0  1  X  X X+1  X X+1 X+1  1  X  X  1 X+1 X+1  X  0 X+1  X  1  X X+1  X  1  0  X  X  1  0  X  1

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+130x^40+178x^41+469x^42+698x^43+902x^44+1256x^45+1603x^46+2078x^47+2571x^48+3016x^49+3507x^50+4108x^51+4547x^52+4858x^53+4999x^54+5002x^55+4676x^56+4428x^57+3790x^58+3238x^59+2732x^60+2044x^61+1509x^62+1042x^63+802x^64+520x^65+335x^66+192x^67+139x^68+82x^69+41x^70+22x^71+12x^72+2x^73+3x^74+4x^75

The gray image is a linear code over GF(2) with n=108, k=16 and d=40.
This code was found by Heurico 1.11 in 193 seconds.