The generator matrix

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

generates a code of length 7 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+6x^6+16x^7+7x^8+2x^10

The gray image is a code over GF(2) with n=28, k=5 and d=12.
This code was found by Heurico 1.16 in 0.000131 seconds.