The generator matrix

 1  0  0  1  1  1  2  0  X  1  1
 0  1  0  1  X X+3  1  1  1  2  0
 0  0  1  1  1  0 X+1  X  X  0  0
 0  0  0  X  0 X+2  X X+2  0  X  2
 0  0  0  0  2  0  2  0  2  2  0
 0  0  0  0  0  2  0  2  2  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+37x^6+152x^7+201x^8+1312x^9+761x^10+3216x^11+843x^12+1312x^13+159x^14+152x^15+42x^16+3x^18+1x^20

The gray image is a code over GF(2) with n=44, k=13 and d=12.
This code was found by Heurico 1.16 in 0.0993 seconds.