The generator matrix
1 0 1 1 1 0 1 1 0 1 1 X 1 1 0 1 1 0 1 1 1 0 X 0 1 1 1 1 0 1 0 1 1
0 1 1 0 1 1 0 1 1 X X+1 1 0 X+1 1 0 X+1 1 0 0 X+1 1 1 1 X+1 0 X+1 X+1 1 X+1 1 X+1 0
0 0 X 0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X X X 0 0 X X 0 X 0 0 0 0 X X
0 0 0 X 0 0 0 0 0 X 0 0 0 0 X X X X X 0 X 0 0 X 0 X 0 0 X 0 X X X
0 0 0 0 X 0 0 0 0 0 X 0 X 0 0 X X X 0 X 0 0 X X 0 X 0 X X X X 0 0
0 0 0 0 0 X 0 0 0 0 0 X X 0 0 X 0 0 X X 0 X X 0 0 X X 0 X X 0 0 0
0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X X X X X 0 X 0 X X 0 X X 0 0
0 0 0 0 0 0 0 X 0 0 X 0 X X X X 0 0 0 X X X 0 X 0 0 0 X X 0 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X X X X 0 X 0 0 X 0 0 X X X 0 X X X 0 X 0 0
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+33x^24+14x^25+67x^26+48x^27+113x^28+136x^29+113x^30+208x^31+189x^32+212x^33+198x^34+208x^35+114x^36+136x^37+90x^38+48x^39+49x^40+14x^41+39x^42+13x^44+5x^46
The gray image is a linear code over GF(2) with n=66, k=11 and d=24.
This code was found by Heurico 1.16 in 0.244 seconds.