The generator matrix

 1  1  1  1  1  1  1  X  1  0  1  1  1  1  X  0  X  0  X  0  X  X  X  X  1  1  1
 0  X  0 X+2  0 X+2  0  X X+2  X  0  2 X+2 X+2 X+2  X X+2  X X+2  X X+2 X+2  0  0  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  2  0  0  2  0  2  2  0  0  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  0  2  0  2  2  2  0  0  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0  0  2  2  0  2  0  2  2  0  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  0  2  2  0  0  2  2  0  0  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  2  2  0  0  0  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+210x^16+160x^18+2x^19+32x^21+440x^22+410x^23+312x^24+1184x^25+32x^26+1828x^27+320x^28+1632x^29+336x^30+740x^31+181x^32+224x^33+90x^35+56x^38+2x^39

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 1.03 seconds.