The generator matrix

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

generates a code of length 14 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+222x^8+658x^9+1560x^10+4668x^11+6588x^12+13110x^13+11928x^14+13096x^15+6569x^16+4702x^17+1608x^18+604x^19+188x^20+26x^21+8x^22

The gray image is a code over GF(2) with n=56, k=16 and d=16.
This code was found by Heurico 1.13 in 3.43 seconds.