The generator matrix

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

generates a code of length 12 over Z2[X]/(X^4) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+36x^11+52x^12+36x^13+1x^14+1x^16+1x^18

The gray image is a linear code over GF(2) with n=96, k=7 and d=44.
This code was found by Heurico 1.16 in -6.48e-008 seconds.