The generator matrix

 1  0  1  1  1 X+2  1  1  1  2  0  2  1  0
 0  1  1  0 X+3  1  X X+3  0  1  1  1 X+1  1
 0  0  X  0 X+2  2  0  0  X X+2 X+2  2  2 X+2
 0  0  0  X  0  2 X+2  X  X  2  X X+2  2  0
 0  0  0  0  2  2  2  2  0  2  0  0  0  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+69x^10+64x^11+329x^12+320x^13+500x^14+320x^15+301x^16+64x^17+69x^18+9x^20+2x^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 0.351 seconds.