The generator matrix

 1  0  0  1  1  1  0  X  1  1 X+2  X  1  1  1  1  2  2  0  0  1  1  1  X X+2  1  1
 0  1  0  0  1  1  1  X  3  X  1  1 X+2 X+1 X+1  3 X+2 X+2  1  2 X+1  3  2  1  1 X+2 X+3
 0  0  1  1  0  3  1  1  0  2 X+3  X  3  1 X+1 X+2  1  1  X  1 X+3  1 X+3  2  0  3  3
 0  0  0  X  2  X  X  X X+2 X+2  2 X+2  2 X+2  0  X X+2  0  2 X+2  X  2  2  0  X  X 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+136x^23+213x^24+332x^25+274x^26+244x^27+215x^28+316x^29+134x^30+92x^31+50x^32+24x^33+6x^34+8x^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 1.11 in 0.0306 seconds.