The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  1 X^2+X+2 X^2+2  X X^2+2  1  X
 0  1  0  0 X^2  3  1  1 X^2+1 X^2+X X+2  1 X+2  1  1  2  1
 0  0  1  0 X^2+1  1 X^2 X^2+1 X+1 X+2 X^2+X+3 X^2  1 X^2+X X+3 X^2+1  3
 0  0  0  1  1 X^2 X^2+1  3 X+1  1 X+2 X^2+X+1 X^2+X+3  2 X^2 X+2 X^2+1

generates a code of length 17 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+538x^13+2347x^14+6092x^15+15293x^16+16804x^17+15626x^18+6136x^19+2116x^20+498x^21+67x^22+12x^23+6x^24

The gray image is a code over GF(2) with n=136, k=16 and d=52.
This code was found by Heurico 1.16 in 6.45 seconds.