The generator matrix

 1  0  1  1  1 X+2  1  1  1  1
 0  1 X+1 X+2  1  1  0  0 X+2  0
 0  0  2  0  0  0  2  2  0  0
 0  0  0  2  0  0  2  0  2  0
 0  0  0  0  2  0  2  2  2  0
 0  0  0  0  0  2  2  2  0  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+25x^6+128x^8+256x^9+207x^10+256x^11+124x^12+23x^14+3x^16+1x^18

The gray image is a code over GF(2) with n=40, k=10 and d=12.
This code was found by Heurico 1.16 in 0.00198 seconds.