The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  1  2  1  1  1
 0  1  1 X+2 X+3  1  2 X+1  1  2  2  3  1  1 X+3  1
 0  0  X  0 X+2  2  X  0  X  2  X  2  X X+2 X+2  2
 0  0  0  2  2  2  0  0  0  0  2  2  2  2  0  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+34x^13+83x^14+130x^15+28x^16+124x^17+74x^18+28x^19+2x^20+2x^21+3x^22+2x^23+1x^24

The gray image is a code over GF(2) with n=64, k=9 and d=26.
This code was found by Heurico 1.16 in 0.00361 seconds.