The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+96x^9+405x^10+1012x^11+1842x^12+3218x^13+3138x^14+3312x^15+1964x^16+956x^17+297x^18+108x^19+32x^20+2x^21+1x^24

The gray image is a code over GF(2) with n=56, k=14 and d=18.
This code was found by Heurico 1.13 in 0.386 seconds.