The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+48x^5+196x^6+754x^7+2105x^8+750x^9+188x^10+46x^11+6x^12+2x^13

The gray image is a code over GF(2) with n=64, k=12 and d=20.
This code was found by Heurico 1.16 in 0.016 seconds.