The generator matrix

 1  0  0  0  1  1  1  X  1  1  1
 0  1  0  0  X  3  1  1 X+1 X+3  0
 0  0  1  0 X+1  1  X X+1  1  0  2
 0  0  0  1  1  X X+1  3  1  X  0

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+68x^7+201x^8+418x^9+943x^10+816x^11+974x^12+428x^13+174x^14+60x^15+8x^16+2x^17+3x^18

The gray image is a code over GF(2) with n=44, k=12 and d=14.
This code was found by Heurico 1.16 in 0.0399 seconds.