The generator matrix

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

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+52x^13+194x^14+264x^15+315x^16+408x^17+337x^18+242x^19+156x^20+52x^21+20x^22+4x^23+1x^26+2x^27

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 0.0292 seconds.