The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  1  0  X  0  1  1  1  0  0  0  X  1  1  1  0  X  1  1  X  1  1  1  1  1  1  X  1  X
 0  1  0  1  0  1  1  0  0  1 X+1  X  1  1  0  X  1 X+1  0  0  1  1  1 X+1  1  1  1 X+1  1  0  X  0 X+1  1  0  X  1  X  0
 0  0  1  1  1  0  1  0  1 X+1  X  1  X  1  1  0  1 X+1  1  1  0  1  0  1  X  X  1  1  X  1  0  0  0  1  0  1  1  1  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  0  0  0  X  0  0  X  X  X  0  0  X  X  X  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  0  0  0  0  0  X  X  X  0  X  X  X  X  0  X  0  0  0  X
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  0  X  0  X  X  X  X  X  X  0  0  X  X  X  0  X  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  X  0  0  X  0  X  X  X  0  X  X  X  X  0  X  0  0  X  X  0  X
 0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  0  0  0  X  0  0  X  X  0  X  X  X  X  X  0  0  X  0  0  0  0  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  X  0  X  X  X  0  X  0  0  X  0  0  X  X  X  0  0  0  0  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+116x^30+273x^32+434x^34+559x^36+625x^38+714x^40+612x^42+414x^44+222x^46+74x^48+34x^50+11x^52+5x^54+2x^56

The gray image is a linear code over GF(2) with n=78, k=12 and d=30.
This code was found by Heurico 1.16 in 1.23 seconds.