The generator matrix

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

generates a code of length 78 over Z2[X]/(X^2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+152x^68+392x^70+479x^72+466x^74+463x^76+444x^78+412x^80+382x^82+313x^84+210x^86+178x^88+106x^90+78x^92+14x^94+2x^96+2x^98+2x^100

The gray image is a linear code over GF(2) with n=156, k=12 and d=68.
This code was found by Heurico 1.16 in 2.87 seconds.