The generator matrix

 1  0  0  1  1  1  2  1  1  1  2  1 X+2 X+2
 0  1  0  1  X X+3  1  0  2  3  1  1  X  1
 0  0  1  1  1  0 X+1  X X+1  0  X  1  1  1
 0  0  0  X  0 X+2  X X+2 X+2  0  2  2 X+2 X+2
 0  0  0  0  2  0  2  0  2  0  2  0  2  0
 0  0  0  0  0  2  0  0  0  2  2  0  2  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+48x^9+212x^10+368x^11+1279x^12+1120x^13+2136x^14+1120x^15+1279x^16+368x^17+212x^18+48x^19+1x^28

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 0.271 seconds.