The generator matrix
1 0 1 1 1 0 1 1 2 1 1 X 2 1 1 1
0 1 1 0 X+1 1 0 X+3 1 X+1 X+2 1 X 2 X 0
0 0 X 0 0 X X 0 X+2 X X+2 0 2 X X 0
0 0 0 X 0 X X X+2 2 X X X+2 X+2 0 0 0
0 0 0 0 2 0 0 0 2 0 0 2 2 0 2 0
0 0 0 0 0 2 0 2 0 0 2 0 2 2 2 2
0 0 0 0 0 0 2 0 0 0 2 2 2 2 0 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+50x^10+114x^11+187x^12+440x^13+1013x^14+1466x^15+1628x^16+1536x^17+945x^18+454x^19+225x^20+72x^21+39x^22+14x^23+7x^24+1x^26
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 0.351 seconds.