The generator matrix

 1  1  1  1  1  1  X  1  0  1  X  1  1
 0  X  0 3X+2 2X X+2 3X+2  2  X  0 3X+2 2X+2  0
 0  0 2X+2  0 2X  2 2X 2X+2 2X  2  2 2X+2  0
 0  0  0 2X+2 2X+2  2  2  0 2X 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+98x^10+112x^11+486x^12+672x^13+476x^14+112x^15+71x^16+18x^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 10.7 seconds.