The generator matrix

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

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+60x^26+68x^27+205x^28+248x^29+375x^30+428x^31+477x^32+562x^33+551x^34+738x^35+683x^36+744x^37+602x^38+608x^39+586x^40+420x^41+338x^42+184x^43+142x^44+64x^45+55x^46+20x^47+16x^48+10x^49+3x^50+2x^51+1x^52+1x^60

The gray image is a linear code over GF(2) with n=72, k=13 and d=26.
This code was found by an older version of Heurico in 0 seconds.