The generator matrix

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

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+26x^4+160x^5+869x^6+1984x^7+869x^8+160x^9+26x^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 -3.24e-008 seconds.