The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 X X X 1 X 0 X 1 0 1 1 1 X 1 1 0 0 1 1 X 1 X X 1 1
0 1 0 0 0 1 1 1 0 0 1 X+1 1 1 0 X+1 X 1 X X+1 1 0 X 0 X 0 1 X 1 X+1 0 1 1 1 1 0 0
0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 1 1 0 X 0 1 1 X+1 X 1 X 0 1 X 1 X X 1 X+1 1 0 0
0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 X+1 X+1 X 1 0 1 X+1 0 X X 1 X+1 X+1 X+1 0 X 1 1 X+1 1 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X 0 X X 0 X 0 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 0 0 X X X X X 0 0 0 X X X X X X X 0 0 X X X 0 X 0
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X 0 X 0 0 X 0 X 0 0 X X X 0 X X 0 0 0 X X X 0
0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 X 0 X 0 0 X X X 0 X 0 0 0 X X X 0 X X X 0 0
0 0 0 0 0 0 0 0 X 0 0 0 X 0 X 0 X 0 X X X X 0 X X 0 X X 0 0 X X X X 0 0 0
0 0 0 0 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 X 0 X 0 X 0 X X 0 X 0 X X 0 X X 0
0 0 0 0 0 0 0 0 0 0 X X X 0 0 X 0 0 0 X X 0 X X X 0 0 0 X 0 0 X 0 X 0 X 0
generates a code of length 37 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+49x^24+30x^25+206x^26+208x^27+462x^28+574x^29+899x^30+1144x^31+1520x^32+1876x^33+2221x^34+2716x^35+2754x^36+3196x^37+2822x^38+2800x^39+2388x^40+1958x^41+1570x^42+1128x^43+815x^44+518x^45+415x^46+184x^47+185x^48+40x^49+49x^50+12x^51+16x^52+8x^54+1x^56+2x^58+1x^60
The gray image is a linear code over GF(2) with n=74, k=15 and d=24.
This code was found by Heurico 1.16 in 47.1 seconds.