The generator matrix

 1  0  0  1  1  1  X  1  1  1
 0  1  0  1 X+2 X+3  1  X  0 X+2
 0  0  1  1 X+3 X+2  1  1 X+1 X+1
 0  0  0  2  0  0  2  0  2  0
 0  0  0  0  2  0  2  0  0  2
 0  0  0  0  0  2  2  2  2  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+79x^6+112x^7+526x^8+656x^9+1339x^10+656x^11+552x^12+112x^13+53x^14+9x^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 0.203 seconds.