The generator matrix

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

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+66x^13+164x^14+260x^15+349x^16+382x^17+376x^18+248x^19+96x^20+62x^21+36x^22+4x^23+2x^24+2x^25

The gray image is a code over GF(2) with n=68, k=11 and d=26.
This code was found by Heurico 1.16 in 5.53 seconds.