The generator matrix

 1  0  0  1  1  1  X  1  1  2  1  1  0  1  1  1
 0  1  0  0  3 X+1  1 X+2 X+3  1  X  1  1  1 X+1 X+2
 0  0  1 X+1 X+3  0  1 X+1  1  3  X  X  X X+2 X+2  3
 0  0  0  2  2  2  0  0  0  2  2  0  2  2  0  2

generates a code of length 16 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+78x^13+185x^14+182x^15+179x^16+184x^17+106x^18+56x^19+36x^20+10x^21+5x^22+2x^23

The gray image is a code over GF(2) with n=64, k=10 and d=26.
This code was found by Heurico 1.16 in 0.0083 seconds.