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.