The generator matrix
1 0 1 1 1 X^2+X 1 1 1
0 1 X+1 X^2+X X^2+1 1 X^3+X^2 0 X^2+X
0 0 X^3 0 0 X^3 X^3 X^3 0
0 0 0 X^3 0 X^3 X^3 0 0
0 0 0 0 X^3 X^3 X^3 X^3 X^3
generates a code of length 9 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+22x^6+96x^7+490x^8+832x^9+488x^10+96x^11+20x^12+2x^14+1x^16
The gray image is a linear code over GF(2) with n=72, k=11 and d=24.
This code was found by Heurico 1.16 in -1.01e-007 seconds.