The generator matrix

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

generates a code of length 54 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+26x^38+74x^39+117x^40+172x^41+306x^42+416x^43+623x^44+744x^45+873x^46+1006x^47+1324x^48+1504x^49+1735x^50+1922x^51+2064x^52+2380x^53+2203x^54+2120x^55+2056x^56+2138x^57+1816x^58+1578x^59+1384x^60+1056x^61+888x^62+638x^63+499x^64+388x^65+291x^66+158x^67+104x^68+60x^69+41x^70+18x^71+19x^72+6x^73+12x^74+6x^75+1x^76+1x^78

The gray image is a linear code over GF(2) with n=108, k=15 and d=38.
This code was found by Heurico 1.16 in 97.8 seconds.