The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  0  1  1  1  1  1  1 X+2  1 X+2 X+2  1  1  1 X+2
 0  1  1  0 X+3  1  X X+3  1  1 X+2  1  1  2 X+1  0  3 X+1 X+1  1  2  1  1 X+2 X+3 X+2  1
 0  0  X  0 X+2  0  0  2  2  0  0  2  0  X  0  X X+2 X+2 X+2  X  2  X X+2  2  0 X+2  X
 0  0  0  X  0  0 X+2 X+2 X+2  X  2 X+2  2  2  2  X  X  X  2 X+2 X+2  2  2  2  X  X X+2
 0  0  0  0  2  0  2  0  0  2  0  2  2  0  2  0  0  0  2  2  0  0  2  0  2  2  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  2  0  2  0  2  2  0  2  0  0  2  2  0  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+186x^22+112x^23+453x^24+384x^25+664x^26+544x^27+651x^28+384x^29+418x^30+112x^31+130x^32+44x^34+13x^36

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 73 seconds.