The generator matrix

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

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+77x^4+96x^5+168x^6+1344x^7+203x^8+96x^9+56x^10+7x^12

The gray image is a code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 3.81e-009 seconds.