The generator matrix

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

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+214x^14+352x^15+927x^16+1088x^17+996x^18+352x^19+124x^20+38x^22+4x^24

The gray image is a code over GF(2) with n=136, k=12 and d=56.
This code was found by Heurico 1.16 in 126 seconds.