The generator matrix

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

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+50x^6+272x^7+790x^8+1352x^9+4286x^10+2880x^11+4272x^12+1392x^13+782x^14+240x^15+57x^16+8x^17+2x^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 0.316 seconds.