The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0  0  0  0  2  X  X  X  X X+2  0  0
 0  0  X  0  0  0 X+2  X X+2  X X+2  2  0  0
 0  0  0  X  0  0  X  0  2  2 X+2 X+2  0  0
 0  0  0  0  X  0  X  2  2  X  0  X  0  0
 0  0  0  0  0  X  X  2 X+2  0  2 X+2  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+330x^8+352x^10+693x^12+5440x^14+693x^16+352x^18+330x^20+1x^28

The gray image is a code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.34 seconds.