The generator matrix
1 0 1 1 1 1 X^2+X 1 1 1 X
0 1 X+1 X^2+X X^2+X+3 X^2+1 1 3 X+1 X^2+1 0
0 0 2 0 0 0 0 2 0 2 2
0 0 0 2 0 0 2 2 0 2 0
0 0 0 0 2 0 0 2 2 0 2
0 0 0 0 0 2 0 2 2 2 0
generates a code of length 11 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+98x^8+256x^9+1040x^10+1280x^11+1096x^12+256x^13+48x^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 15.6 seconds.