The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+334x^8+1496x^10+6500x^12+6000x^14+1833x^16+184x^18+36x^20

The gray image is a code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.16 in 0.935 seconds.