The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 X X X X 0 1 X 1 1 X X 1 0 1 1 1 0 1 1 0 X 1 X 0 0 0 1 1 1 0 1 1 1 0 1 1
0 1 0 0 0 1 1 1 0 0 1 X+1 1 0 1 1 X X 1 X+1 X+1 X X 0 1 1 X 0 1 1 X+1 1 1 0 1 0 0 X X 1 1 X X+1 1 X X X 0
0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 X 1 0 1 X+1 1 1 0 1 1 X X 1 0 X X 1 X+1 1 X 0 1 1 0 0 X+1 1 X X+1 1 1 0 0
0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 X X 1 0 X 1 X+1 1 0 1 1 0 X+1 X+1 0 X+1 X+1 X X+1 X+1 1 X X 0 0 X+1 X+1 X+1 X X+1 X+1 1 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 X X 0 0 X 0 X X X 0 X X 0 0 X X 0 X 0 X 0 X 0 0 0 X X X X 0 0
0 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X X 0 0 X X 0 X 0 X X X 0 X X 0 0 0 0 0 0 X 0 X 0 0 X 0 X X X 0
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X X 0 X X 0 X 0 0 X X 0 X X 0 0 X 0 0 0 X X 0 0 X 0 0 X X 0 0 0 X 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X 0 X X X 0 0 0 0 0 X X X X 0 X X 0 0 0 0 X X X X X X 0 0 X X X 0
0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 X X X X 0 X 0 X X 0 0 X X 0 0 X X 0 X X X 0 X 0 X 0 0 0 0 0
0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X X X 0 0 X X 0 0 X X X X X 0 0 X 0 X 0 0 0 X X 0 0 X 0 0 0 0
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 X X 0 0 X 0 0 0 X 0 X 0 0 X X 0 X 0 0 0 X X 0 X X 0 X 0
generates a code of length 48 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+35x^34+64x^35+213x^36+258x^37+433x^38+552x^39+800x^40+970x^41+1249x^42+1500x^43+1811x^44+2160x^45+2258x^46+2614x^47+2628x^48+2624x^49+2441x^50+2322x^51+1861x^52+1618x^53+1306x^54+916x^55+712x^56+490x^57+383x^58+208x^59+145x^60+60x^61+66x^62+14x^63+19x^64+12x^65+20x^66+2x^67+2x^68+1x^70
The gray image is a linear code over GF(2) with n=96, k=15 and d=34.
This code was found by Heurico 1.16 in 77.7 seconds.