The generator matrix

 1  0  1  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  2
 0  0 X^2 X^2+2  2 X^2+2

generates a code of length 6 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+29x^4+226x^5+517x^6+220x^7+26x^8+2x^9+3x^10

The gray image is a code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 0 seconds.