The generator matrix
1 0 1 1 1 0 X 1 1 X
0 1 1 0 X+1 1 0 0 0 0
0 0 X X+2 0 X+2 X 0 0 0
0 0 0 2 0 0 0 0 0 2
0 0 0 0 2 0 0 0 0 2
0 0 0 0 0 2 0 0 0 2
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
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+85x^4+432x^6+128x^7+2858x^8+1920x^9+5536x^10+1920x^11+2858x^12+128x^13+432x^14+85x^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 0.175 seconds.