The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+62x^10+110x^11+259x^12+324x^13+528x^14+368x^15+225x^16+92x^17+70x^18+2x^19+3x^20+4x^22

The gray image is a code over GF(2) with n=56, k=11 and d=20.
This code was found by Heurico 1.16 in 0.0199 seconds.