The generator matrix

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

generates a code of length 10 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+93x^4+192x^5+480x^6+960x^7+1314x^8+2944x^9+4416x^10+2944x^11+1314x^12+960x^13+480x^14+192x^15+93x^16+1x^20

The gray image is a code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.15 seconds.