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.