The generator matrix

 1  1  1  1  2  0  1
 0  X  0  X  X  X  0
 0  0  X  X X^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+19x^4+78x^5+159x^6+520x^7+148x^8+70x^9+25x^10+4x^11

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 -3.24e-008 seconds.