The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+72x^6+216x^7+726x^8+1840x^9+3300x^10+4048x^11+3296x^12+1920x^13+720x^14+152x^15+73x^16+16x^17+4x^18

The gray image is a code over GF(2) with n=44, k=14 and d=12.
This code was found by Heurico 1.16 in 2.29 seconds.