The generator matrix
1 1 1 1 1 1 1 1 X X X
0 X^3 0 0 0 0 0 X^3 X^3 X^3 0
0 0 X^3 0 0 0 X^3 X^3 X^3 X^3 X^3
0 0 0 X^3 0 0 X^3 0 0 X^3 X^3
0 0 0 0 X^3 0 X^3 0 X^3 X^3 0
0 0 0 0 0 X^3 X^3 0 X^3 0 X^3
generates a code of length 11 over Z2[X]/(X^4) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+34x^8+24x^10+384x^11+48x^12+8x^14+13x^16
The gray image is a linear code over GF(2) with n=88, k=9 and d=32.
This code was found by Heurico 1.16 in -3.24e-008 seconds.