The generator matrix
1 0 0 1 1 1 X^2+X+2 1 1 1 1
0 1 0 1 X X^2+X+1 1 X+2 2 3 X+3
0 0 1 1 X^2+1 X X+1 X^2+X+1 0 X^2+1 X^2+X
0 0 0 X^2+2 X^2 2 X^2 X^2+2 X^2 2 X^2+2
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+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 0.422 seconds.