The generator matrix

 1  1  1  1  1  1  1  X  1  1  1  1  1  X
 0  X  0  0  0  0  0  0  X  2  0 X+2  X  2
 0  0  X  0  0  0  0 X+2  X  0  X  0  2  2
 0  0  0  X  0  0  0  X X+2 X+2  2  2  2  0
 0  0  0  0  X  0  X  2  X X+2 X+2 X+2  0  0
 0  0  0  0  0  X  X X+2  2  X X+2  X  0  0
 0  0  0  0  0  0  2  0  0  0  0  2  2  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+386x^8+500x^10+2132x^12+2048x^13+6332x^14+2048x^15+1873x^16+812x^18+212x^20+36x^22+4x^24

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 0.97 seconds.