The generator matrix
1 1 1 1 1 1 X 0 1 1 X X^3
0 X 0 X^2+X X^2 X^3+X^2+X X^2+X X X^3+X^2 X X^3+X^2+X X
0 0 X^3+X^2 0 X^2 X^2 X^3 X^3 0 X^2 X^2 X^3+X^2
0 0 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3
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+182x^10+128x^11+412x^12+128x^13+164x^14+3x^16+6x^18
The gray image is a linear code over GF(2) with n=96, k=10 and d=40.
This code was found by Heurico 1.16 in 0 seconds.