The generator matrix
1 1 1 1 1 1 1 1 1 1 X 1 1
0 2X+2 0 2X+2 0 2X 2X+2 2 0 2X+2 2X+2 2X 0
0 0 2X 0 0 2X 0 0 0 2X 2X 0 2X
0 0 0 2X 0 0 0 2X 2X 2X 0 2X 2X
0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 0
generates a code of length 13 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+23x^10+74x^12+320x^13+70x^14+20x^16+3x^18+1x^24
The gray image is a code over GF(2) with n=104, k=9 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.