The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 X X X X 0 X 1 1 1 1 1 1 1 1 X X 0 0 1 0 0 1 0 0 X 0 1
0 1 0 0 0 1 1 1 0 0 1 X+1 1 0 1 1 X 1 0 0 X 0 1 X+1 X+1 X+1 X X X 1 1 0 0 X+1 1 1 1 1 0
0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 X 1 1 1 X 1 0 0 X+1 X+1 0 0 1 1 1 X+1 X 1 X 0 0 1 0 0
0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 X X 0 X+1 X+1 X X 1 1 0 0 1 1 X 1 X+1 1 0 X 1 X 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 X X 0 X 0 X X X 0 X 0 0 0 X X X 0 X X 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X 0 X X 0 0 X 0 0 X 0 X 0 X X X X 0 X X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X X 0 X 0 0 X 0 0 X 0 X X 0 0 0 X X X X 0 X 0 X X
0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X 0 X X X 0 X X 0 0 0 0 X 0 0 X 0 X 0 0 0 X X X
0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 0 X X X X 0 X X X 0 X 0 X 0 X 0 X X X X 0
0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X X 0 0 X 0 X 0 0 X 0 0 X X 0 0 X X 0 0 0 0
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X 0 0 X X 0 X 0 0 0 X 0 X X X X 0 0 0 X 0 0
generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.
Homogenous weight enumerator: w(x)=1x^0+40x^26+58x^27+186x^28+206x^29+460x^30+556x^31+904x^32+1140x^33+1453x^34+1974x^35+2266x^36+2730x^37+2899x^38+2968x^39+2782x^40+2792x^41+2330x^42+2070x^43+1595x^44+1138x^45+834x^46+508x^47+385x^48+164x^49+161x^50+58x^51+64x^52+22x^53+15x^54+8x^56+1x^60
The gray image is a linear code over GF(2) with n=78, k=15 and d=26.
This code was found by Heurico 1.16 in 53.6 seconds.