The generator matrix

 1  0  1  1  1  0  X  X  1  1
 0  1  1  0 X+1  1  0  2  0  0
 0  0  X  0  X  0  X  X  0  0
 0  0  0  X  X X+2  X  0  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+480x^6+128x^7+1314x^8+896x^9+2368x^10+896x^11+1314x^12+128x^13+480x^14+93x^16+1x^20

The gray image is a code over GF(2) with n=40, k=13 and d=8.
This code was found by Heurico 1.16 in 0.047 seconds.