The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  0  1  1  1  1  0  0  1  0  1  X  X  0  X  1  1
 0  1  0  0  0  0  0  0  0  1  1  1  1 X+1  1 X+1  X  1 X+1  X  0  1  1  0  1  0  0
 0  0  1  0  0  0  1  1  1  1  1  0  0 X+1  0  1  X  1  0  1 X+1  X  X  1  1  0  0
 0  0  0  1  0  1  1  0  1  0  1  1  1  1  0  0  1  0  0  1 X+1 X+1  X  X X+1  0  0
 0  0  0  0  1  1  0  1  1  0  1  1  0  X  1  1 X+1 X+1  0  X  X  X  0  X X+1  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  0  0
 0  0  0  0  0  0  X  0  0  0  0  X  0  X  0  0  X  X  0  X  0  X  0  X  X  X  0
 0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  0  X  0  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  0  0  0  X  X  X  X  0  X  0  0  X  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  0  0  X  0  X  0  0  X  0  X  X  0  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+65x^16+96x^17+268x^18+442x^19+631x^20+952x^21+1454x^22+1984x^23+2466x^24+2886x^25+3256x^26+3500x^27+3382x^28+3128x^29+2468x^30+1944x^31+1424x^32+1028x^33+676x^34+298x^35+211x^36+96x^37+62x^38+24x^39+12x^40+6x^41+8x^42

The gray image is a linear code over GF(2) with n=54, k=15 and d=16.
This code was found by Heurico 1.16 in 23.5 seconds.