The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  1  X  2  0 X+2  1  1  1  1  1  X  X  1  X
 0  1  1 X+2 X+3  1  2 X+1  1  X  3  1  2 X+1  1  1  1  1 X+2 X+3  X  0 X+1  1 X+2  0  0
 0  0  X  0 X+2  0  X  2 X+2 X+2  2  X X+2  2  X  X  0  2  0  X  2  2  0  0 X+2 X+2  0
 0  0  0  2  0  0  0  2  0  2  0  2  2  2  2  0  0  0  0  2  0  2  2  0  2  2  2
 0  0  0  0  2  0  0  0  2  2  0  0  2  2  0  0  2  2  2  0  2  2  2  0  2  0  0
 0  0  0  0  0  2  2  0  0  0  2  0  2  0  2  2  0  2  2  0  0  2  2  0  2  0  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+73x^22+96x^23+223x^24+160x^25+373x^26+240x^27+339x^28+208x^29+175x^30+48x^31+68x^32+16x^33+15x^34+9x^36+4x^38

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 0.0737 seconds.