The generator matrix

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

generates a code of length 17 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+241x^12+420x^13+1406x^14+1440x^15+3448x^16+2360x^17+3556x^18+1584x^19+1335x^20+324x^21+222x^22+16x^23+31x^24

The gray image is a code over GF(2) with n=68, k=14 and d=24.
This code was found by Heurico 1.13 in 0.629 seconds.