The generator matrix

 1  0  1  1  1 X^2+X X^3+X^2 X^3+X^2+X  X  1
 0  1 X+1 X^3+X^2+X X^2+1  1  1  1 X^3  0
 0  0 X^2 X^2  0  0 X^3 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  0 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+24x^6+96x^7+233x^8+1052x^9+1273x^10+1068x^11+242x^12+84x^13+14x^14+4x^15+4x^16+1x^18

The gray image is a linear code over GF(2) with n=80, k=12 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.