The generator matrix

 1  0  0  0  1  1  1  1  0 X+2  2
 0  1  0  0  0  3  2 X+1  1 X+2  1
 0  0  1  0  1  1  X  0 X+1  X X+2
 0  0  0  1  1  X X+1 X+1  2  1 X+1
 0  0  0  0  2  0  0  2  2  2  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+124x^7+423x^8+980x^9+1472x^10+2136x^11+1559x^12+1000x^13+368x^14+108x^15+16x^16+4x^17+1x^20

The gray image is a code over GF(2) with n=44, k=13 and d=14.
This code was found by Heurico 1.16 in 6.84 seconds.