The generator matrix

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

generates a code of length 15 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+138x^13+84x^14+136x^15+15x^16+84x^17+28x^18+24x^19+2x^21

The gray image is a code over GF(2) with n=60, k=9 and d=26.
This code was found by Heurico 1.16 in 0.137 seconds.