The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+32x^27+160x^28+228x^29+523x^30+654x^31+854x^32+1224x^33+1570x^34+1916x^35+2169x^36+2606x^37+2746x^38+2994x^39+2937x^40+2736x^41+2388x^42+1978x^43+1671x^44+1142x^45+823x^46+548x^47+365x^48+238x^49+130x^50+66x^51+31x^52+16x^53+12x^54+4x^55+3x^56+2x^57+1x^60

The gray image is a linear code over GF(2) with n=78, k=15 and d=27.
This code was found by Heurico 1.16 in 76 seconds.