The generator matrix

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

generates a code of length 11 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+403x^8+1000x^9+3492x^10+6584x^11+3526x^12+984x^13+372x^14+8x^15+14x^16

The gray image is a code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.16 in 0.39 seconds.