The generator matrix

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

generates a code of length 7 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+346x^4+1184x^5+6437x^6+16832x^7+6437x^8+1184x^9+346x^10+1x^14

The gray image is a code over GF(2) with n=56, k=15 and d=16.
This code was found by Heurico 1.16 in 8.47 seconds.