The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  2  X
 0 2X+2  0  0 2X 2X+2  0 2X+2  2  2  0 2X 2X+2
 0  0 2X+2  0 2X+2 2X+2 2X  2  0  2 2X+2 2X 2X
 0  0  0 2X+2  2 2X  0 2X+2 2X+2  0 2X+2 2X+2 2X

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+62x^10+24x^11+273x^12+336x^13+236x^14+24x^15+53x^16+14x^18+1x^20

The gray image is a code over GF(2) with n=104, k=10 and d=40.
This code was found by Heurico 1.16 in 0.125 seconds.