The generator matrix

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

generates a code of length 7 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+8x^5+31x^6+176x^7+31x^8+8x^9+1x^14

The gray image is a code over GF(2) with n=56, k=8 and d=20.
This code was found by Heurico 1.16 in 6.87e-008 seconds.