The generator matrix

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

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+12x^10+32x^11+38x^12+32x^13+11x^14+1x^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 0.000693 seconds.