The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 0 1 X 1 0 1 1 X 1 1 X X 0 X 1 1 X 1 0 1 1 1 1 1 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X 1 1 X+1 1 X 0 X 1 X+1 1 1 1 0 1 X 1 0 1 X+1 0 0 1 X X
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 1 X X 1 0 X 1 1 X 1 0 X 1 1 0 1 0 X+1 X 1 1 0 X 0
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 0 X+1 X 1 0 1 X 1 X+1 0 0 X 1 X+1 0 0 X X+1 1 X 1 0 X 1 0
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 1 1 X 0 X+1 1 X X+1 X+1 X+1 0 X+1 0 X X+1 1 X 0 X+1 X 1 X+1 X+1 0 X+1
0 0 0 0 0 X 0 0 X 0 X X X X X 0 X X 0 0 X X X 0 X X 0 0 X X 0 X X X X 0 0 X 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 X X X 0 X 0 0 X X X 0 0 0 X X 0 0 X X X 0 X X 0 X
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X 0 X X X
generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 30.
Homogenous weight enumerator: w(x)=1x^0+198x^30+572x^32+928x^34+1082x^36+1294x^38+1316x^40+1141x^42+946x^44+500x^46+175x^48+34x^50+4x^52+1x^74
The gray image is a linear code over GF(2) with n=78, k=13 and d=30.
This code was found by Heurico 1.16 in 4.68 seconds.