The generator matrix

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

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+54x^13+96x^14+114x^15+173x^16+188x^17+160x^18+100x^19+48x^20+46x^21+32x^22+10x^23+2x^24

The gray image is a code over GF(2) with n=68, k=10 and d=26.
This code was found by Heurico 1.16 in 0.0139 seconds.