The generator matrix

 1  0  0  1  1  1  0  0  X X+2  1  1  1  1
 0  1  0  1  X X+3  1  1  1  0  2  0  1  0
 0  0  1  1  1  0 X+3  X  1  1  0  X X+1  0
 0  0  0  X  0 X+2 X+2  X  0  2  X  X X+2  0
 0  0  0  0  2  0  0  2  2  0  2  0  0  0
 0  0  0  0  0  2  0  2  2  2  2  0  2  0
 0  0  0  0  0  0  2  2  0  0  2  2  0  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+34x^8+108x^9+370x^10+848x^11+2132x^12+2572x^13+4134x^14+2752x^15+2157x^16+772x^17+350x^18+112x^19+28x^20+4x^21+10x^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 0.596 seconds.