The generator matrix

 1  0  0  1  1  1 X^2  1 X^2+X+2 X^2+2  1 X^2+X  1  1  1 X^2+X  1
 0  1  0 X^2 X^2+1  1  1  X X^2  1 X^2+X+3  1 X^2+X  X X+1  1 X+1
 0  0  1 X^2+X+1 X+1 X^2  1 X+2  1 X^2+X X^2+X X+1 X^2+1 X^2  1 X^2+1 X+1
 0  0  0  2  2  0  2  0  0  0  2  0  0  2  2  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+338x^14+848x^15+1747x^16+2432x^17+1646x^18+784x^19+348x^20+32x^21+14x^22+2x^26

The gray image is a code over GF(2) with n=136, k=13 and d=56.
This code was found by Heurico 1.16 in 0.141 seconds.