The generator matrix

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

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+108x^8+152x^9+378x^10+612x^11+1922x^12+3404x^13+3418x^14+3144x^15+1811x^16+784x^17+478x^18+84x^19+62x^20+12x^21+14x^22

The gray image is a code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 0.897 seconds.