The generator matrix

 1  1  1  1  1  1  1  1  X  1
 0  X  0  0  0  X X+2  2  X  0
 0  0  X  0  X  X  X  2  0  0
 0  0  0  X  X  2 X+2  0  X  0
 0  0  0  0  2  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+33x^6+36x^7+56x^8+224x^9+327x^10+216x^11+68x^12+32x^13+23x^14+4x^15+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 0.00322 seconds.