The generator matrix

 1  0  1  1  1  1  1
 0  1 X+1 X+2  0 X+2  0
 0  0  2  0  2  0  0
 0  0  0  2  2  0  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+16x^4+8x^5+62x^6+80x^7+67x^8+8x^9+10x^10+4x^12

The gray image is a code over GF(2) with n=28, k=8 and d=8.
This code was found by Heurico 1.16 in 0.000204 seconds.