The generator matrix
1 0 0 1 1 1 X 1 1 2 1 X+2 2 1 1 1
0 1 0 1 X+2 X+3 1 0 3 1 X 1 1 3 X+1 X
0 0 1 1 X+3 X+2 1 X+2 X+1 X 1 X+1 1 X+1 0 1
0 0 0 2 0 0 0 0 0 0 2 2 2 2 2 0
0 0 0 0 2 0 0 0 0 2 2 0 2 2 0 2
0 0 0 0 0 2 0 0 2 2 0 0 2 2 0 0
0 0 0 0 0 0 2 0 2 0 0 2 0 2 0 2
0 0 0 0 0 0 0 2 2 2 0 2 2 2 2 2
generates a code of length 16 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+72x^10+80x^11+544x^12+1040x^13+1712x^14+2976x^15+3529x^16+2976x^17+1736x^18+1040x^19+520x^20+80x^21+64x^22+14x^24
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 12.6 seconds.