The generator matrix

 1  0  0  0  0  1  1  1 X+2  1  1  1  1
 0  1  0  0  0  2  2  X  1  X  1 X+3  0
 0  0  1  0  0 X+2  1 X+3  1  1 X+1  2  2
 0  0  0  1  0 X+1  1  2 X+1 X+1  1 X+2  2
 0  0  0  0  1  1  X  3  3 X+1 X+1  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+324x^8+404x^9+1972x^10+3764x^11+5846x^12+8040x^13+5976x^14+3784x^15+1987x^16+388x^17+244x^18+4x^19+34x^20

The gray image is a code over GF(2) with n=52, k=15 and d=16.
This code was found by Heurico 1.13 in 1.18 seconds.