The generator matrix

 1  0  0  1  1  1  X  1  1  1 3X+2  1  1
 0  1  0  X  3 X+3  1 X+2 2X+2  0  1 2X+1 2X
 0  0  1  1 X+1  X  1 3X+3 2X+1 X+2  X 3X+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+90x^10+342x^11+866x^12+1566x^13+786x^14+322x^15+101x^16+10x^17+12x^18

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 0.016 seconds.