The generator matrix

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

generates a code of length 7 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+16x^4+56x^5+158x^6+560x^7+163x^8+56x^9+10x^10+4x^12

The gray image is a code over GF(2) with n=56, k=10 and d=16.
This code was found by Heurico 1.16 in 3.62e-008 seconds.