The generator matrix
1 0 0 1 1 1 X 1
0 1 0 1 2 3 1 0
0 0 1 1 0 X+1 1 0
0 0 0 X 3X+2 2X+2 0 2X
generates a code of length 8 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+82x^4+316x^5+1501x^6+6184x^7+16557x^8+6272x^9+1474x^10+280x^11+96x^12+4x^13+1x^14
The gray image is a code over GF(2) with n=64, k=15 and d=16.
This code was found by Heurico 1.16 in 0.36 seconds.