The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+11x^2+41x^4+331x^6+256x^7+331x^8+41x^10+11x^12+1x^14

The gray image is a code over GF(2) with n=28, k=10 and d=4.
This code was found by Heurico 1.16 in 0.000611 seconds.