The generator matrix
1 0 0 1 1 1 1 1
0 1 0 1 3X+2 3X+3 2X X+3
0 0 1 1 X+1 X X+1 X
0 0 0 2 0 2X 2 2X+2
generates a code of length 8 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 5.
Homogenous weight enumerator: w(x)=1x^0+160x^5+828x^6+3360x^7+7693x^8+3360x^9+812x^10+160x^11+10x^12
The gray image is a code over GF(2) with n=64, k=14 and d=20.
This code was found by Heurico 1.16 in 0.14 seconds.