The generator matrix

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

generates a code of length 7 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+7x^4+12x^5+10x^6+72x^7+5x^8+12x^9+6x^10+3x^12

The gray image is a code over GF(2) with n=28, k=7 and d=8.
This code was found by Heurico 1.16 in 0.000161 seconds.