The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  1  1  X  1  0  1  X  1  0  0  1  0  0
 0  1  0  1  0  1  1  0  0  1  1  1  1  0  X  1  1  X  0 X+1  1  X  1  0  0  1  0
 0  0  1  1  1  0  1  0  1  1  0  0  1  1  X  1 X+1 X+1  1  0  1  1  0  1  0  0  1
 0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  0  0  0  X  X  0  X  0  X  0  0  X  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  0  X  0  0  X  X  0  X  X  0  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  0  X  X  X  0  0  X  0  X  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  X  0  X  0  0  0  X  0  X  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  X  0  0  X  X  0  X  0  X  0
 0  0  0  0  0  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  0  X  X  0  X

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+179x^16+212x^18+1391x^20+2364x^22+5441x^24+6344x^26+7863x^28+4472x^30+3024x^32+932x^34+469x^36+12x^38+59x^40+5x^44

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 22.6 seconds.