The generator matrix
1 1 1 1 0 1 1 2X X 1 1
0 X 0 X X 2X 2 2 3X 2X 2X
0 0 X X 2X+2 2 X X X+2 2X 3X+2
0 0 0 2X 0 2X 0 2X 2X 0 0
0 0 0 0 2X 2X 2X 2X 2X 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+194x^8+192x^9+944x^10+1408x^11+1000x^12+192x^13+144x^14+21x^16
The gray image is a code over GF(2) with n=88, k=12 and d=32.
This code was found by Heurico 1.16 in 20.1 seconds.