The generator matrix

 1  0  0  0  1  1  1  X  1  1
 0  1  0  0  X  3  1  1 X+1  0
 0  0  1  0 X+1  1  X X+1  1  2
 0  0  0  1  1  X X+1  3  1  2

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+52x^6+186x^7+347x^8+1104x^9+733x^10+1076x^11+354x^12+192x^13+46x^14+2x^15+2x^16+1x^18

The gray image is a code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0296 seconds.