The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  1 X+2  0  X  0 X+2  1  1  1  1 X+2  1  1  1  1  2
 0  1  0  0  0  1  2  3  1  2 X+1 X+3  1  X  1  1 X+2  2  0 X+1  3  1  X X+1  3  0 X+2
 0  0  1  0  0  1  3  2  3 X+1  1  0  3  1 X+2  1  1  X X+2  2  2  0  3  3  X X+1  1
 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  1  0  X  2 X+2  2  1 X+3
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  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+318x^22+384x^23+955x^24+672x^25+1240x^26+944x^27+1433x^28+752x^29+858x^30+272x^31+260x^32+48x^33+44x^34+7x^36+4x^38

The gray image is a code over GF(2) with n=108, k=13 and d=44.
This code was found by Heurico 1.13 in 0.485 seconds.