The generator matrix

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

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+118x^22+230x^23+428x^24+368x^25+654x^26+596x^27+556x^28+410x^29+404x^30+158x^31+115x^32+20x^33+22x^34+8x^35+4x^36+2x^37+2x^38

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 0.237 seconds.