The generator matrix

 1  1  1  1  X  0  1  1  1  1
 0  X  0 X+2  X  X  0  2  0  0
 0  0  2  0  0  0  0  2  2  0
 0  0  0  2  0  0  2  2  2  0
 0  0  0  0  2  0  2  2  0  0
 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+18x^6+64x^8+128x^9+92x^10+128x^11+60x^12+18x^14+3x^16

The gray image is a code over GF(2) with n=40, k=9 and d=12.
This code was found by Heurico 1.16 in 0.00104 seconds.