The generator matrix

 1  1  1  1  1  1  1  X 2X  X  2  X  1
 0  X  0  X 2X  0 3X  2 2X+2  X  X  X  0
 0  0  X  X  2 X+2 X+2  X  X  X 3X  2  0
 0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 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+87x^10+228x^11+378x^12+700x^13+330x^14+220x^15+91x^16+4x^17+7x^18+2x^20

The gray image is a code over GF(2) with n=104, k=11 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.