The generator matrix

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

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+20x^6+18x^7+31x^8+112x^9+665x^10+108x^11+30x^12+16x^13+18x^14+2x^15+2x^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 6.87e-008 seconds.