The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+23x^10+74x^12+64x^13+70x^14+20x^16+3x^18+1x^24

The gray image is a code over GF(2) with n=52, k=8 and d=20.
This code was found by Heurico 1.16 in 0.00131 seconds.