The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  1  1  X  1  X  X  1  1  1
 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  0  X  0  X  X  0  0  X  X  X  X  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  0  X  X  X  0  X  0  0  X  0  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  0  X  X  X  0  0  X  X  X  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  0  X  X  X  0  X  0  0  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  0  0  X  X  0  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  0  X  0  0  X  X  X  0  X  0  X  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  X  X  X  X  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  X  X  X  0  X  X  X  0  X  0  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  0  X  X  0  0  X  X  X  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+176x^16+226x^20+64x^22+750x^24+640x^26+1250x^28+320x^30+431x^32+182x^36+50x^40+6x^44

The gray image is a linear code over GF(2) with n=54, k=12 and d=16.
This code was found by Heurico 1.16 in 0.679 seconds.