The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  1 X+2  0  X  0 X+2  1  1 X+2  1  2 X+2  2  1  1  1
 0  1  0  0  0  1  2  3  1  2 X+1 X+3  1  X  1  1 X+2  2  0  1  X  1 X+2  1  1 X+2 X+1
 0  0  1  0  0  1  3  2  3 X+1  1  0  3  1 X+2  1  1  X X+2  2  0 X+1 X+2  2 X+2 X+3 X+2
 0  0  0  1 X+1  2 X+3 X+1 X+1  X  1  2 X+2  1  1  1 X+3  0  3  0 X+2  2  1 X+1  3 X+2  0
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  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+289x^22+452x^23+765x^24+968x^25+1120x^26+1076x^27+1140x^28+872x^29+769x^30+420x^31+228x^32+48x^33+30x^34+4x^35+10x^36

The gray image is a code over GF(2) with n=108, k=13 and d=44.
This code was found by Heurico 1.16 in 2.01 seconds.