The generator matrix

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

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+150x^22+60x^23+274x^24+116x^25+370x^26+152x^27+382x^28+136x^29+170x^30+44x^31+133x^32+4x^33+46x^34+10x^36

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 1.78 seconds.