The generator matrix

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

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+124x^13+634x^14+1372x^15+3747x^16+4696x^17+3684x^18+1368x^19+604x^20+108x^21+34x^22+12x^23

The gray image is a code over GF(2) with n=136, k=14 and d=52.
This code was found by Heurico 1.16 in 0.453 seconds.