The generator matrix

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

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+132x^9+354x^10+1044x^11+1743x^12+3176x^13+3456x^14+3176x^15+1822x^16+1044x^17+282x^18+132x^19+17x^20+4x^22+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 1.16 in 2.8 seconds.