The generator matrix

 1  0  0  1  1  1  0  1  1  X  1 X+2  1  2  0 X+2  0
 0  1  0  0  1  1  1 X+1  X  1  X  1 X+1 X+2  X  2  1
 0  0  1  1  0 X+1  1  1 X+2  1  1  X X+2  1  X  1  1
 0  0  0  X X+2  2  X X+2  X  2  0  X  0  X X+2 X+2 X+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+78x^13+200x^14+182x^15+445x^16+252x^17+448x^18+188x^19+160x^20+54x^21+24x^22+14x^23+2x^24

The gray image is a code over GF(2) with n=68, k=11 and d=26.
This code was found by Heurico 1.11 in 0.0134 seconds.