The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  0  1  1  1  1 X+2  1  0  1  1 X+2  1  0  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0  1 X+1 X+2  3  3  1  0  1 X+2 X+1  1 X+1  1 X+2
 0  0  2  0  0  0  0  0  0  2  2  0  2  0  0  0  2  2  0  2  0  0  2  2  2  2  0
 0  0  0  2  0  0  0  2  0  2  2  0  0  2  2  0  2  0  2  0  2  0  2  0  0  2  0
 0  0  0  0  2  0  0  0  2  0  2  0  2  2  2  2  2  0  0  2  0  2  0  0  2  0  0
 0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  0  2  2  0  0  0  2  0  2  0  2
 0  0  0  0  0  0  2  2  0  2  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  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+82x^22+48x^23+234x^24+192x^25+335x^26+288x^27+330x^28+192x^29+210x^30+48x^31+69x^32+8x^34+6x^36+4x^38+1x^42

The gray image is a code over GF(2) with n=108, k=11 and d=44.
This code was found by Heurico 1.16 in 28.8 seconds.