The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  1  1  X  0  1  X  1  1
 0  X  0 X+2  0 X+2  0 X+2  2 X+2  0 X+2  0 X+2  X  0  2  2  0  2 X+2 X+2  X X+2 X+2  X  0
 0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  0  0  2  2  2  0  2  2  0
 0  0  0  2  0  0  0  2  0  0  0  2  0  2  0  2  2  2  2  0  2  0  0  2  0  2  0
 0  0  0  0  2  0  0  0  0  2  2  2  0  2  2  0  2  2  0  0  2  2  2  0  0  0  2
 0  0  0  0  0  2  0  2  0  2  2  0  2  2  0  0  2  0  0  2  0  2  2  2  0  0  0
 0  0  0  0  0  0  2  0  2  0  2  2  0  0  2  2  0  2  2  0  2  2  0  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+64x^22+132x^24+64x^25+193x^26+128x^27+197x^28+64x^29+116x^30+51x^32+6x^34+2x^36+4x^38+1x^42+1x^44

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 0.313 seconds.