The generator matrix

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

generates a code of length 27 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+148x^23+175x^24+350x^25+226x^26+350x^27+227x^28+276x^29+86x^30+104x^31+44x^32+46x^33+6x^34+6x^35+1x^36+2x^38

The gray image is a code over GF(2) with n=108, k=11 and d=46.
This code was found by Heurico 1.16 in 0.0641 seconds.