The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+58x^10+32x^11+273x^12+320x^13+249x^14+32x^15+45x^16+12x^18+1x^20+1x^22

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 0.063 seconds.