The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 1 0 1 X 1
0 X 0 X^2+X X^2 X^2+X+2 X^2+2 X 0 2 X^2+X+2 X^2+2 X^2+X X X^2+2 X^2+X+2 0
0 0 X^2+2 0 X^2 X^2 2 X^2 0 X^2 X^2 0 2 2 X^2 X^2+2 0
0 0 0 2 2 0 2 2 2 2 0 0 0 2 0 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+64x^14+88x^15+168x^16+400x^17+152x^18+88x^19+51x^20+8x^22+3x^24+1x^28
The gray image is a code over GF(2) with n=136, k=10 and d=56.
This code was found by Heurico 1.16 in 6.87e-008 seconds.