The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 X 1 1 1 1 X 0 X 1 1 1 1 0 1 1 0 1 0 0
0 1 0 0 0 0 0 0 0 1 1 1 1 X 1 X+1 X 0 X X 1 1 X+1 X 0 1 0 X+1 1 0 1 X X
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X 1 X 0 X 1 1 1 X X 1 X X+1 0 X+1 X+1 1 0 1 1
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 X+1 1 1 X X X 1 X+1 X+1 X 1 1 1 X 0 X+1 X 1 X+1
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X+1 X+1 0 0 X+1 X X+1 0 X X+1 X X X 1 X+1 1 0 0 1 1
0 0 0 0 0 X 0 0 X 0 X X X 0 0 0 X 0 X 0 0 0 X X X 0 X 0 0 X 0 0 X
0 0 0 0 0 0 X 0 0 0 0 0 X X X 0 X X 0 X 0 X X X X 0 X 0 0 0 0 0 X
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X 0 X X X X
generates a code of length 33 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+104x^24+128x^25+237x^26+308x^27+399x^28+540x^29+570x^30+666x^31+729x^32+760x^33+717x^34+776x^35+624x^36+512x^37+426x^38+276x^39+170x^40+104x^41+93x^42+20x^43+17x^44+4x^45+4x^46+2x^47+4x^48+1x^50
The gray image is a linear code over GF(2) with n=66, k=13 and d=24.
This code was found by Heurico 1.16 in 3.51 seconds.