The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 X 1 1 1 1 1 0 1 1 0 1 X 1 1 1 X 1 1 0 X 1 1 X 1
0 1 0 0 0 0 0 0 0 1 1 1 1 X 1 X+1 X X 0 X+1 1 X+1 X+1 0 1 1 X 0 1 1 0 1 1 1 X X+1 1 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X 1 X 0 1 X 0 X+1 X+1 X 1 0 1 X 1 X+1 X+1 1 X 0 1 X+1 X+1 1 0
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 X+1 1 1 X X X 0 X+1 1 X X X+1 X+1 0 X X+1 1 X X+1 0 X+1 X 0 0
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X+1 X+1 0 0 X X+1 0 X+1 0 1 X+1 1 X+1 X X X+1 0 X+1 0 1 X+1 0 1 0 0
0 0 0 0 0 X 0 0 X 0 X X X 0 0 0 X X 0 X 0 0 X X 0 X 0 0 X X X X 0 0 0 X 0 X
0 0 0 0 0 0 X 0 0 0 0 0 X X X 0 X 0 X 0 X 0 0 X X X X X 0 0 0 0 X 0 0 X 0 X
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X 0 0 0 0 0
generates a code of length 38 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.
Homogenous weight enumerator: w(x)=1x^0+58x^28+106x^29+184x^30+264x^31+339x^32+396x^33+457x^34+562x^35+649x^36+682x^37+708x^38+730x^39+642x^40+630x^41+526x^42+406x^43+300x^44+212x^45+156x^46+86x^47+57x^48+22x^49+17x^50+1x^52+1x^64
The gray image is a linear code over GF(2) with n=76, k=13 and d=28.
This code was found by Heurico 1.16 in 4.22 seconds.