The generator matrix

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

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+94x^26+94x^27+483x^28+502x^29+992x^30+1182x^31+1832x^32+2292x^33+3147x^34+3872x^35+4369x^36+5232x^37+5371x^38+6088x^39+5533x^40+5660x^41+4387x^42+3962x^43+3227x^44+2234x^45+1902x^46+1066x^47+915x^48+432x^49+329x^50+120x^51+143x^52+32x^53+31x^54+7x^56+3x^58+2x^60

The gray image is a linear code over GF(2) with n=78, k=16 and d=26.
This code was found by Heurico 1.11 in 112 seconds.