The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+94x^7+591x^8+2592x^9+7285x^10+11564x^11+7466x^12+2512x^13+522x^14+134x^15+6x^16+1x^18

The gray image is a code over GF(2) with n=88, k=15 and d=28.
This code was found by Heurico 1.16 in 0.812 seconds.