The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  1  X X+2  1  X  X  1  1  1  0  1  0 X+2 X+2  1
 0  1  0  0  2  1  3  1 X+2  2 X+3 X+1  0  1  1  3 X+2  2  X  X  2  1 X+3  1  1  1  2
 0  0  1  0  3  1  2  3  0 X+1 X+3 X+2  1 X+3  2  X  1  1  3 X+2 X+3  2 X+2 X+1 X+2  1  X
 0  0  0  1  1  2  3  3 X+1  X X+3  0 X+2  2  3  1  3  1 X+1  3  3 X+2  1 X+3 X+1 X+2  0

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+66x^22+246x^23+507x^24+450x^25+589x^26+454x^27+606x^28+404x^29+420x^30+188x^31+102x^32+42x^33+13x^34+6x^35+2x^39

The gray image is a code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.16 in 0.208 seconds.