The generator matrix

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

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+36x^27+141x^28+272x^29+472x^30+664x^31+933x^32+1206x^33+1530x^34+1766x^35+2250x^36+2654x^37+2825x^38+2938x^39+2857x^40+2900x^41+2327x^42+1936x^43+1621x^44+1204x^45+870x^46+524x^47+352x^48+182x^49+156x^50+70x^51+36x^52+30x^53+9x^54+2x^55+1x^56+3x^58

The gray image is a linear code over GF(2) with n=78, k=15 and d=27.
This code was found by Heurico 1.11 in 25.1 seconds.