The generator matrix
1 1 1 1 1 1 1 1 X X X X 2
0 2X+2 0 2X+2 2X 2 2X 2 2X+2 2X+2 0 2X 0
0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X
generates a code of length 13 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+36x^12+64x^13+16x^14+11x^16
The gray image is a code over GF(2) with n=104, k=7 and d=48.
This code was found by Heurico 1.16 in 0 seconds.