The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 34.

Homogenous weight enumerator: w(x)=1x^0+31x^34+56x^35+71x^36+76x^37+53x^38+44x^39+34x^40+34x^41+13x^42+14x^43+22x^44+16x^45+11x^46+8x^47+13x^48+2x^49+4x^50+6x^51+3x^52

The gray image is a linear code over GF(2) with n=78, k=9 and d=34.
This code was found by Heurico 1.16 in 0.0258 seconds.