The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X 1
0 2 0 2 0 2 2X 2X+2 0 2X 2X 2 0
0 0 2X 0 0 2X 2X 2X 2X 2X 0 0 0
0 0 0 2X 2X 2X 2X 0 2X 0 2X 0 0
generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+1x^10+16x^11+30x^12+160x^13+30x^14+16x^15+1x^18+1x^24
The gray image is a code over GF(2) with n=104, k=8 and d=40.
This code was found by Heurico 1.16 in 0 seconds.