The generator matrix

 1  1  1  1  1  1  1  1 X^2  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^3 X^2  0
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2  0 X^2  0
 0  0  0  0 X^3 X^3 X^3 X^3 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+33x^6+36x^7+56x^8+480x^9+839x^10+472x^11+68x^12+32x^13+23x^14+4x^15+3x^16+1x^18

The gray image is a linear code over GF(2) with n=80, k=11 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.