The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+38x^4+142x^5+824x^6+2090x^7+825x^8+130x^9+40x^10+6x^11

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 -1.01e-007 seconds.