The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+9x^10+34x^11+45x^12+28x^13+6x^14+2x^15+2x^16+1x^22

The gray image is a linear code over GF(2) with n=48, k=7 and d=20.
This code was found by Heurico 1.16 in 0.000552 seconds.