The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+122x^14+474x^15+793x^16+1466x^17+642x^18+382x^19+158x^20+46x^21+12x^22

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 0.046 seconds.