The generator matrix

1 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 X 0 1 1 1 0 1 1 1 0 X X 1 X 1 1 X 0 1 0 0 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X 1 1 X+1 X+1 X+1 1 1 1 X+1 1 1 X 1 1 1 0 X X 1
0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 X X+1 1 0 1 X+1 X 1 X+1 0 X X X+1 1 X X 0 X+1 1 0 X X
0 0 0 1 0 0 0 1 1 1 0 X X 1 X+1 X+1 1 1 0 1 X+1 1 0 0 1 1 1 X+1 0 1 X X X 1 X+1 X+1 X X X
0 0 0 0 1 0 1 0 X+1 1 1 0 X+1 0 X+1 1 X 1 X X+1 0 X+1 1 0 X X X 1 X X 0 X+1 X+1 X+1 X 0 1 X+1 X
0 0 0 0 0 1 1 X+1 X 1 X 1 1 0 X+1 0 1 0 0 0 X 1 1 X+1 1 0 X+1 0 X+1 X+1 X X X X+1 1 0 X X+1 X
0 0 0 0 0 0 X X 0 0 0 0 X 0 0 0 X X X X X 0 0 X 0 X X X 0 0 0 X 0 X 0 X X 0 0

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+218x^30+549x^32+850x^34+1190x^36+1266x^38+1337x^40+1208x^42+845x^44+498x^46+160x^48+54x^50+12x^52+2x^54+1x^56+1x^60

The gray image is a linear code over GF(2) with n=78, k=13 and d=30.
This code was found by Heurico 1.10 in 1.58 seconds.