The generator matrix

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

generates a code of length 55 over Z2[X]/(X^2) who�s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+111x^38+341x^40+568x^42+128x^43+770x^44+490x^45+978x^46+788x^47+1357x^48+1188x^49+1399x^50+1892x^51+1387x^52+2310x^53+1355x^54+2662x^55+1212x^56+2492x^57+1343x^58+1878x^59+1363x^60+1312x^61+1319x^62+670x^63+1164x^64+358x^65+825x^66+158x^67+477x^68+40x^69+250x^70+16x^71+109x^72+2x^73+41x^74+11x^76+3x^78

The gray image is a linear code over GF(2) with n=110, k=15 and d=38.
This code was found by Heurico 1.16 in 99.6 seconds.