The generator matrix

 1  1  1  1  X X^2  X  X  X  X
 0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0  0
 0  0 X^3  0  0  0 X^3 X^3  0  0
 0  0  0 X^3  0  0 X^3 X^3 X^3  0
 0  0  0  0 X^3  0  0 X^3 X^3  0
 0  0  0  0  0 X^3 X^3  0 X^3 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+25x^6+16x^7+64x^8+240x^9+335x^10+240x^11+60x^12+16x^13+23x^14+3x^16+1x^18

The gray image is a linear code over GF(2) with n=80, k=10 and d=24.
This code was found by Heurico 1.16 in -3.24e-008 seconds.