The generator matrix

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

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+32x^6+122x^7+242x^8+390x^9+468x^10+400x^11+252x^12+104x^13+28x^14+6x^15+1x^16+2x^17

The gray image is a code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.11 in 0.00352 seconds.