The generator matrix
1 0 0 1 1 1 1 1
0 1 0 1 X+2 X+3 3X 2
0 0 1 1 X+1 X X+2 X
0 0 0 2X 0 0 2X 2X
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+42x^5+537x^6+1496x^7+4045x^8+1492x^9+534x^10+40x^11+2x^12+2x^13+1x^14
The gray image is a code over GF(2) with n=64, k=13 and d=20.
This code was found by Heurico 1.16 in 0.031 seconds.