The generator matrix

 1  1  1  1  X  1  1
 0 X^2+2  0  0  0  2 X^2
 0  0 X^2+2  0  0 X^2  2
 0  0  0 X^2+2 X^2+2 X^2+2 X^2+2
 0  0  0  0  2  2  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+77x^4+296x^6+1280x^7+331x^8+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 0.015 seconds.