The generator matrix

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

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+26x^7+60x^8+90x^9+202x^10+276x^11+188x^12+100x^13+52x^14+18x^15+7x^16+2x^17+2x^18

The gray image is a code over GF(2) with n=44, k=10 and d=14.
This code was found by Heurico 1.16 in 0.0047 seconds.