The generator matrix

 1  0  0  1  1  1  2
 0  1  0  1  X X+2  1
 0  0  1  1  1  3  X
 0  0  0  X  0 X+2  2

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+60x^4+192x^5+440x^6+648x^7+473x^8+176x^9+48x^10+8x^11+2x^12

The gray image is a code over GF(2) with n=28, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00281 seconds.