The generator matrix

 1  0  0  1  1  1  X  X  1  1  1  0  1  1  X  1  1  1  1  2  1  2  1  1  X X+2  2
 0  1  0  0  1  1  1  1 X+1  X  1  1  X  2  0  X X+1  2 X+1  1  0  X  X  1  1  X  1
 0  0  1 X+1 X+3  0  1  X X+3  1  X X+3  X  1  1 X+1 X+1  X  2  X  1  1  X X+1  3  1  X
 0  0  0  2  0  0  0  0  0  2  0  0  0  2  0  2  0  2  2  2  0  2  2  2  2  0  0
 0  0  0  0  2  0  0  0  2  0  0  0  2  2  2  2  0  2  0  0  2  2  2  0  2  0  2
 0  0  0  0  0  2  0  2  2  2  0  2  0  0  0  2  2  2  0  2  2  2  0  2  0  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+142x^22+216x^23+362x^24+520x^25+511x^26+608x^27+556x^28+480x^29+345x^30+200x^31+97x^32+24x^33+25x^34+8x^36+1x^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 0.234 seconds.