The generator matrix

 1  0  0  1  1  1  1
 0  1  0  X 2X+3 3X+2  0
 0  0  1  1 X+1 2X+3  0

generates a code of length 7 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+59x^4+280x^5+597x^6+2226x^7+594x^8+276x^9+59x^10+2x^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 2.1e-008 seconds.