The generator matrix

 1  1  1  1  0  0  2
 0  X  0  X  X  X  X
 0  0  X  X X^2+2  0 X^2
 0  0  0  2  0  2  2
 0  0  0  0  2  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+122x^4+160x^5+773x^6+1984x^7+773x^8+160x^9+122x^10+1x^14

The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.015 seconds.