The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^4+256x^5+696x^6+2056x^7+729x^8+240x^9+48x^10+8x^11+2x^12

The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.016 seconds.