The generator matrix

 1  0  0  1  1  1  1
 0  1  0  1 X+2  0  2
 0  0  1  1 X+1 X+1  2
 0  0  0  2  0  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+32x^4+74x^5+256x^6+302x^7+253x^8+70x^9+32x^10+2x^11+2x^12

The gray image is a code over GF(2) with n=28, k=10 and d=8.
This code was found by Heurico 1.16 in 0.000943 seconds.