The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X
 0  2  0  0  0  0  0  0  0  0  2  2  2
 0  0  2  0  0  0  0  0  0  2  2  2  0
 0  0  0  2  0  0  0  0  0  2  0  2  2
 0  0  0  0  2  0  0  0  2  0  0  2  2
 0  0  0  0  0  2  0  0  2  0  2  0  2
 0  0  0  0  0  0  2  0  2  2  2  0  0
 0  0  0  0  0  0  0  2  2  2  0  0  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+55x^8+224x^12+512x^13+128x^14+87x^16+16x^20+1x^24

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 0.00383 seconds.