The generator matrix

 1  1  1  1  X  X  1
 0  X  0  X X^2 X^2+2 X^2+X
 0  0  X  X  X  X  0
 0  0  0 X^2  0 X^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+60x^4+256x^5+696x^6+2056x^7+729x^8+240x^9+48x^10+8x^11+2x^12

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.