The generator matrix

 1  1  X  1  1  1  1
 0  2  2  0  0  0  0
 0  0 2X  0  0  0  0
 0  0  0 2X  0  0  0
 0  0  0  0 2X  0  0
 0  0  0  0  0 2X  0
 0  0  0  0  0  0 2X

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

Homogenous weight enumerator: w(x)=1x^0+11x^2+41x^4+331x^6+1280x^7+331x^8+41x^10+11x^12+1x^14

The gray image is a code over GF(2) with n=56, k=11 and d=8.
This code was found by Heurico 1.16 in 0 seconds.