The generator matrix

 1  1  1  1 X^2  X  1
 0  X X^2+2 X^2+X X^2+2  0  0
 0  0  2  0  2  2  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+15x^4+20x^5+146x^6+152x^7+141x^8+20x^9+14x^10+3x^12

The gray image is a code over GF(2) with n=56, k=9 and d=16.
This code was found by Heurico 1.16 in -6.48e-008 seconds.