The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+144x^13+342x^14+546x^15+683x^16+690x^17+708x^18+508x^19+276x^20+156x^21+38x^22+2x^23+2x^25

The gray image is a code over GF(2) with n=68, k=12 and d=26.
This code was found by Heurico 1.16 in 0.107 seconds.