The generator matrix
1 0 0 0 1 1 1 1 0 1 1 X 1 X X 0 1 1 1 1 1 X X X 0 1 0 X X 0 X 1 1
0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0 0 X 1 X 1 1 1 0 1 0 1 1 1 0 1 0 0
0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 X 0 0 1 1 X+1 0 1 X+1 1 X 0 X+1 1 0 0 0
0 0 0 1 1 1 0 0 1 1 0 1 X+1 X X+1 1 X 1 1 0 0 X X+1 X X+1 X+1 X 1 X+1 0 1 0 0
0 0 0 0 X 0 0 0 0 0 0 0 X 0 X X 0 0 X 0 X X 0 X 0 X X 0 0 0 0 0 0
0 0 0 0 0 X 0 0 0 0 0 X X 0 0 X 0 0 X X 0 0 X X X 0 X X X 0 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X X 0 X X X 0 0 X 0 X X 0 0 0 0 X 0 0 0 0
0 0 0 0 0 0 0 X 0 0 0 X X X X X X X X 0 0 0 0 0 X 0 0 X 0 X 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 X X X X X 0 X 0 0 X X X X X X 0 0 0 0
0 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 0 X X 0 X 0 X 0 0 0 X 0 X 0 0 0 0
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X 0 X 0 X X 0 0 X X X 0 0 0 0 0
generates a code of length 33 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+82x^20+42x^21+169x^22+180x^23+445x^24+568x^25+849x^26+1102x^27+1568x^28+2046x^29+2294x^30+2698x^31+2826x^32+3056x^33+2768x^34+2812x^35+2215x^36+1942x^37+1589x^38+1208x^39+892x^40+504x^41+457x^42+182x^43+150x^44+34x^45+60x^46+10x^47+11x^48+6x^50+1x^52+1x^56
The gray image is a linear code over GF(2) with n=66, k=15 and d=20.
This code was found by Heurico 1.16 in 33.8 seconds.