The generator matrix

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

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+215x^8+416x^9+160x^10+896x^11+592x^12+3520x^13+704x^14+896x^15+215x^16+416x^17+160x^18+1x^24

The gray image is a code over GF(2) with n=52, k=13 and d=16.
This code was found by Heurico 1.16 in 0.769 seconds.