The generator matrix

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

generates a code of length 36 over Z2[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+90x^27+212x^28+248x^29+359x^30+400x^31+487x^32+586x^33+618x^34+718x^35+698x^36+746x^37+668x^38+578x^39+557x^40+406x^41+302x^42+240x^43+144x^44+54x^45+37x^46+22x^47+10x^48+8x^49+2x^52+1x^56

The gray image is a linear code over GF(2) with n=72, k=13 and d=27.
This code was found by Heurico 1.16 in 6.66 seconds.