The generator matrix

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

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+75x^4+64x^5+304x^6+1152x^7+319x^8+64x^9+64x^10+5x^12

The gray image is a code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.