The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  X  X  1  X  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  0  0  0  2  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  0  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  2  2  0  0  2  0  0  2  2  2  2  0  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  0  2  0  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  2  2  0  2  0
 0  0  0  0  0  0  0  0  2  0  0  2  0  2  0  0  2  2  0  0  0  2  2  2  0  0  2
 0  0  0  0  0  0  0  0  0  2  0  2  2  2  0  2  2  2  0  2  0  0  0  0  0  2  2
 0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  2  2  2  0  0  2  0  0

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+38x^16+112x^18+145x^20+32x^21+166x^22+192x^23+222x^24+480x^25+306x^26+4736x^27+335x^28+480x^29+284x^30+192x^31+205x^32+32x^33+116x^34+63x^36+30x^38+14x^40+10x^42+1x^44

The gray image is a code over GF(2) with n=108, k=13 and d=32.
This code was found by Heurico 1.16 in 1.18 seconds.