The generator matrix

 1  1  1  1  1  1  1  1  X X^2  1  X  1  1  2  2  1
 0  X  0  X  0  2 X^2+X  X X^2 X^2 X+2 X^2+X X^2  0  X X^2  0
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2  X  X X^2+2  0 X^2+2  0 X^2+2  X X^2+X+2
 0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  0  2
 0  0  0  0  2  2  0  0  2  0  2  2  0  2  0  2  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+56x^13+190x^14+418x^15+907x^16+986x^17+904x^18+396x^19+144x^20+60x^21+26x^22+2x^23+4x^24+2x^25

The gray image is a code over GF(2) with n=136, k=12 and d=52.
This code was found by Heurico 1.16 in 0.062 seconds.