The generator matrix

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

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+189x^14+472x^15+837x^16+1140x^17+842x^18+404x^19+160x^20+28x^21+17x^22+4x^23+2x^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 0.047 seconds.