The generator matrix

 1  0  1  1  1  X  1  1  1  1  0  1  1
 0  1  1  2 3X+1  1 X+3 3X+2 2X+1 3X+3  0  2 3X+2
 0  0  X  X  2  X 3X  2 X+2  0  X 2X+2 2X+2
 0  0  0 2X  0 2X  0 2X 2X 2X  0  0  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+115x^10+384x^11+778x^12+1552x^13+794x^14+352x^15+91x^16+16x^17+11x^18+2x^20

The gray image is a code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 0.031 seconds.