The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  X  1  1  0  1  0  X  0  1
 0  X  0  0  0  X X+2  X  0  2  X X+2  0  2  X  2  2 X+2 X+2  X X+2  0  0  X  0  2  0
 0  0  X  0  X  X  X  2  0  2 X+2 X+2  X X+2  0  X  0  2  2  X  2  2  0 X+2  2  X  0
 0  0  0  X  X  2 X+2 X+2  0 X+2  2 X+2  X  X X+2  2  X  0  2  0 X+2  X  2  0  X X+2  2
 0  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  0  0  0  0  0  2  2  0  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+26x^22+58x^23+111x^24+140x^25+144x^26+154x^27+112x^28+96x^29+65x^30+38x^31+30x^32+20x^33+18x^34+6x^35+2x^36+3x^38

The gray image is a code over GF(2) with n=108, k=10 and d=44.
This code was found by Heurico 1.16 in 0.0313 seconds.