The generator matrix

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

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+84x^27+204x^28+306x^29+351x^30+354x^31+462x^32+612x^33+643x^34+692x^35+721x^36+656x^37+701x^38+664x^39+537x^40+396x^41+309x^42+232x^43+111x^44+78x^45+40x^46+22x^47+11x^48+4x^50+1x^64

The gray image is a linear code over GF(2) with n=72, k=13 and d=27.
This code was found by Heurico 1.10 in 21.6 seconds.