The generator matrix

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

generates a code of length 56 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+41x^38+60x^39+101x^40+166x^41+203x^42+312x^43+412x^44+498x^45+684x^46+848x^47+943x^48+1236x^49+1367x^50+1460x^51+1633x^52+1742x^53+1834x^54+1890x^55+1950x^56+1838x^57+1772x^58+1716x^59+1725x^60+1550x^61+1335x^62+1210x^63+959x^64+820x^65+708x^66+530x^67+359x^68+276x^69+207x^70+144x^71+93x^72+58x^73+37x^74+22x^75+15x^76+6x^77+3x^78+1x^80+2x^81+1x^82

The gray image is a linear code over GF(2) with n=112, k=15 and d=38.
This code was found by Heurico 1.16 in 97.6 seconds.