The generator matrix

 1  0  1  1  1  2  1  1  2  1
 0  1  1  0 X+1  1  0 X+1  1  0
 0  0  X  0  X  2  X  2  X  0
 0  0  0  X  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+26x^6+46x^7+105x^8+212x^9+244x^10+208x^11+110x^12+44x^13+26x^14+2x^15

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 0.00292 seconds.