The generator matrix

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

generates a code of length 36 over Z2[X]/(X^2) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+178x^26+707x^28+1190x^30+1890x^32+2618x^34+3049x^36+2806x^38+2060x^40+1088x^42+559x^44+172x^46+49x^48+12x^50+5x^52

The gray image is a linear code over GF(2) with n=72, k=14 and d=26.
This code was found by Heurico 1.16 in 70.5 seconds.