The generator matrix

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

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+71x^22+300x^23+393x^24+512x^25+507x^26+594x^27+520x^28+474x^29+313x^30+256x^31+100x^32+36x^33+13x^34+2x^35+2x^36+2x^37

The gray image is a code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.11 in 0.102 seconds.