The generator matrix

 1  1  1  1  1 X^3  1  1  1  X X^2  0
 0  X  0 X^3+X^2+X X^2  X  X X^3+X^2 X^2+X X^3  X  X
 0  0 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2  0

generates a code of length 12 over Z2[X]/(X^4) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+52x^10+112x^11+220x^12+64x^13+40x^14+16x^15+3x^16+4x^18

The gray image is a linear code over GF(2) with n=96, k=9 and d=40.
This code was found by Heurico 1.16 in -6.48e-008 seconds.