The generator matrix

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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+128x^38+298x^40+166x^41+528x^42+404x^43+880x^44+808x^45+1240x^46+1256x^47+1506x^48+1876x^49+1684x^50+2352x^51+1867x^52+2588x^53+1905x^54+2364x^55+1768x^56+1994x^57+1615x^58+1326x^59+1213x^60+740x^61+816x^62+312x^63+531x^64+140x^65+240x^66+44x^67+111x^68+8x^69+31x^70+4x^71+16x^72+5x^74+2x^75+1x^76

The gray image is a linear code over GF(2) with n=106, k=15 and d=38.
This code was found by Heurico 1.16 in 99.9 seconds.