The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  X  1  1
 0  X  0  0  0  0  0  0  2 X+2 X+2 X+2  2  2
 0  0  X  0  0  0  X X+2 X+2  X X+2  X  X  0
 0  0  0  X  0  X  X X+2  0  0  2 X+2  0  X
 0  0  0  0  X  X  0 X+2  X  X  X  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  0  2  2
 0  0  0  0  0  0  2  0  0  2  2  0  2  0
 0  0  0  0  0  0  0  2  2  2  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+262x^8+740x^10+2336x^12+2048x^13+5572x^14+2048x^15+2413x^16+716x^18+232x^20+12x^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 1.27 seconds.