The generator matrix

 1  1  1  1  X  X  1
 0  X  0 X+2  X X+2  0
 0  0  2  0  0  2  0
 0  0  0  2  0  2  0
 0  0  0  0  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+18x^4+32x^5+13x^6+128x^7+13x^8+32x^9+18x^10+1x^14

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 0.000251 seconds.