The generator matrix
1 1 1 1 1 1 1 1 X 1
0 X 0 0 0 X X+2 X 0 0
0 0 X 0 X X X+2 0 0 0
0 0 0 X X 0 X+2 X 0 0
0 0 0 0 2 0 0 0 2 0
0 0 0 0 0 2 0 0 2 0
0 0 0 0 0 0 2 0 2 0
0 0 0 0 0 0 0 2 2 0
generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+84x^4+56x^5+232x^6+280x^7+462x^8+688x^9+4600x^10+688x^11+420x^12+280x^13+280x^14+56x^15+57x^16+8x^18
The gray image is a code over GF(2) with n=40, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0632 seconds.