The generator matrix

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

generates a code of length 10 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+245x^6+1596x^7+8336x^8+30176x^9+50391x^10+30104x^11+8396x^12+1600x^13+211x^14+12x^15+3x^16+1x^18

The gray image is a linear code over GF(2) with n=80, k=17 and d=24.
This code was found by Heurico 1.16 in 16.3 seconds.