The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2) 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 0.156 seconds.