The generator matrix

 1  0  0  1  1  1  1  1  1  1
 0  1  0  1  X X+3  0  1  1  0
 0  0  1  1  1  0  X X+1  1  0
 0  0  0  X  0 X+2  X  X  0  2
 0  0  0  0  2  0  2  2  2  2
 0  0  0  0  0  2  2  0  2  2

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+22x^5+131x^6+224x^7+1050x^8+1286x^9+2755x^10+1296x^11+1056x^12+226x^13+121x^14+16x^15+5x^16+2x^17+1x^18

The gray image is a code over GF(2) with n=40, k=13 and d=10.
This code was found by Heurico 1.16 in 0.0672 seconds.