The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  X  1  X  1  X  0  X  1  1  1  1  1  0  1  1  X  1  0  1  1  1  1  1  0  1  X  X
 0  1  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X X+1  1  1  1  1  1  1 X+1  1  1  1 X+1  1  1  0  1
 0  0  1  0  0  0  0  0  0  0  1  1  1 X+1  1 X+1  1  0  X  0  X  X  1 X+1  1 X+1  X  1 X+1  0  1  X  0 X+1  1  1  1  1  0
 0  0  0  1  0  0  0  1  1  1  1 X+1  0  0 X+1  X  1  1  X X+1  0  X  1 X+1  0  X X+1 X+1 X+1  0  X  X  X  0  0  0 X+1 X+1 X+1
 0  0  0  0  1  0  1  1  X X+1  0 X+1  1  1 X+1  0  0 X+1  X  X X+1  X X+1  X  0  X  1  X X+1 X+1 X+1 X+1 X+1  X  X  1  0  0  X
 0  0  0  0  0  1  1  X X+1  1  0  1  1  0  0  1  1  1  1 X+1 X+1  X X+1  0  X X+1  X X+1 X+1  X  0 X+1  0  0  0  0 X+1  0  X
 0  0  0  0  0  0  X  0  X  0  X  0  0  X  0  0  0  X  X  0  0  X  X  0  X  X  0  X  0  0  0  0  X  0  X  0  X  0  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+182x^30+634x^32+810x^34+1186x^36+1233x^38+1361x^40+1212x^42+848x^44+480x^46+186x^48+50x^50+6x^52+1x^54+1x^56+1x^64

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 4.72 seconds.