The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+32x^5+93x^6+204x^7+605x^8+1712x^9+3389x^10+4300x^11+3411x^12+1696x^13+607x^14+228x^15+78x^16+16x^17+7x^18+4x^19+1x^20

The gray image is a code over GF(2) with n=44, k=14 and d=10.
This code was found by Heurico 1.16 in 0.253 seconds.