The generator matrix

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

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+23x^8+76x^10+64x^11+301x^12+128x^13+256x^14+64x^15+84x^16+20x^18+7x^20

The gray image is a code over GF(2) with n=52, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00388 seconds.