The generator matrix
1 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 1 X 1 X X 1 1 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 X 1 X X 1 X+1 X 1 0
0 0 1 0 0 0 0 0 0 1 X X+1 1 X X+1 0 1 0 X X+1 1 1 X 1 X X 0
0 0 0 1 0 0 0 0 1 0 X X+1 X+1 1 X 1 1 X+1 X 0 X X X+1 X 1 0 0
0 0 0 0 1 0 0 0 1 1 X+1 X X+1 X 0 X+1 0 1 X X+1 0 X X X X+1 1 0
0 0 0 0 0 1 0 0 1 X 1 0 X+1 X X+1 0 0 X X+1 X+1 X 1 0 1 X 1 0
0 0 0 0 0 0 1 0 1 X+1 0 X+1 X X 1 1 X+1 1 X+1 1 X+1 1 1 X 0 1 0
0 0 0 0 0 0 0 1 X 1 1 X 0 X+1 X+1 X+1 X 0 X 1 0 0 X X X+1 0 0
generates a code of length 27 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+124x^16+150x^17+672x^18+662x^19+1579x^20+1736x^21+2954x^22+3748x^23+4766x^24+6300x^25+6290x^26+7564x^27+6194x^28+6272x^29+4892x^30+3784x^31+2999x^32+1822x^33+1548x^34+590x^35+571x^36+104x^37+154x^38+36x^39+22x^40+2x^42
The gray image is a linear code over GF(2) with n=54, k=16 and d=16.
This code was found by Heurico 1.11 in 50.3 seconds.