The generator matrix

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

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+72x^7+197x^8+402x^9+959x^10+840x^11+950x^12+412x^13+190x^14+64x^15+4x^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 1.11 in 0.0175 seconds.