The generator matrix

 1  0  1  1  1  2  1  0  1  1  2  1  2  1  0  1  1  1  1  1  1 X+2 X+2  2  2  1  X
 0  1  1  0  1  1  2  1  0 X+1  1 X+1  1  2  1  3 X+3  1  0 X+2  0  1  1  X  1 X+2  2
 0  0  X  0  0  0  0  0  0  2  2  X  X X+2 X+2 X+2  2  X  X  X X+2  X X+2  X  X  X X+2
 0  0  0  X  0  0  2 X+2 X+2  0 X+2  2  2  2 X+2 X+2 X+2 X+2 X+2 X+2  2  0 X+2 X+2  0  X  X
 0  0  0  0  X X+2 X+2  X X+2  0  2 X+2  0  2 X+2  0  0  X X+2  2 X+2 X+2  2  X X+2  0 X+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+226x^22+124x^23+417x^24+388x^25+664x^26+536x^27+635x^28+360x^29+394x^30+108x^31+158x^32+20x^33+60x^34+5x^36

The gray image is a code over GF(2) with n=108, k=12 and d=44.
This code was found by Heurico 1.16 in 1.86 seconds.