The generator matrix
1 1 1 1 1 X X X X X X
0 X^3 0 0 0 X^3 X^3 X^3 X^3 0 0
0 0 X^3 0 X^3 X^3 X^3 0 0 0 X^3
0 0 0 X^3 X^3 0 X^3 X^3 0 X^3 X^3
generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+6x^9+6x^10+104x^11+6x^12+2x^14+1x^16+2x^17
The gray image is a linear code over GF(2) with n=88, k=7 and d=36.
This code was found by Heurico 1.16 in -6.48e-008 seconds.