The generator matrix

 1  0  1  1  1  1  1
 0  1 X+1 X+2 3X+2 2X  0
 0  0 2X+2 2X+2  0  2 2X
 0  0  0 2X 2X 2X  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+31x^4+52x^5+354x^6+1176x^7+349x^8+52x^9+30x^10+3x^12

The gray image is a code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0 seconds.