The generator matrix

 1  0  0  1  1  1 X+2  1  1  0  1  1  1  1
 0  1  0  1  0 X+3  1  1 X+3  1  0  3  X  X
 0  0  1  1  1  0  1  1  2  X X+3  X  0  X
 0  0  0  X  0  0  0  2  X  X  X  2  X X+2
 0  0  0  0  X X+2 X+2  0  X  2 X+2  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+64x^9+192x^10+490x^11+953x^12+1464x^13+1790x^14+1532x^15+989x^16+504x^17+161x^18+42x^19+9x^20+1x^26

The gray image is a code over GF(2) with n=56, k=13 and d=18.
This code was found by Heurico 1.16 in 0.299 seconds.