The generator matrix

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

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+86x^13+171x^14+178x^15+191x^16+180x^17+122x^18+44x^19+24x^20+22x^21+3x^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 1.11 in 0.00413 seconds.