The generator matrix

 1  0  1  1  1 X+2  1  1 2X  1  1 3X  1  1  2  1  1
 0  1 X+1 X+2 2X+3  1 X+3 2X  1 X+2 3X  1 2X+2 X+1  X 3X+2  X
 0  0  2  0 2X+2 2X  2 2X+2  2 2X 2X 2X 2X  0  2  2 2X+2
 0  0  0 2X  0 2X 2X 2X  0  0 2X  0 2X  0 2X  0 2X
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X  0 2X  0  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+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 125 seconds.