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.