The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  1  1  1  0  0  1  1  1  1  1  1  1  1
 0  1  1  0  1  1  0  1  1  0  1  1  0  X X+1 X+1 X+1  1  1  0  0  0  0 X+1  0  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  X  X  0  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  0  0  X  X  X  0  X  X  0  X  X  0  0  0  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  X  X  0  0  X  X  0  0  X  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  X  X  0  X  0  0  X  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  X  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X  X  X  0  0  X  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  0  X  X  0  X  X  0  0  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+152x^16+126x^18+234x^20+32x^21+258x^22+576x^23+568x^24+480x^25+632x^26+1920x^27+708x^28+480x^29+660x^30+576x^31+299x^32+32x^33+254x^34+82x^36+106x^38+4x^40+12x^42

The gray image is a linear code over GF(2) with n=54, k=13 and d=16.
This code was found by Heurico 1.16 in 1.93 seconds.