The generator matrix

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

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+69x^8+164x^9+509x^10+572x^11+502x^12+156x^13+66x^14+4x^15+4x^16+1x^18

The gray image is a code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0 seconds.