The generator matrix
1 1 1 1 1 1 1 1 X 2 X 1 0 1 X^2 1 1
0 X 0 X^2+X+2 2 X^2+X 0 X X^2+X X X^2+X+2 X^2+2 X X+2 X X X
0 0 X^2+2 0 2 X^2+2 X^2 X^2+2 X^2+2 X^2 X^2+2 0 2 X^2 2 2 2
0 0 0 X^2+2 X^2+2 X^2 X^2 2 X^2+2 2 2 2 2 X^2+2 X^2 X^2+2 0
generates a code of length 17 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 14.
Homogenous weight enumerator: w(x)=1x^0+132x^14+192x^15+457x^16+512x^17+442x^18+192x^19+96x^20+16x^22+6x^24+2x^26
The gray image is a code over GF(2) with n=136, k=11 and d=56.
This code was found by Heurico 1.16 in 2.19 seconds.