The generator matrix

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

generates a code of length 49 over Z2[X]/(X^3) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+60x^41+107x^42+124x^43+164x^44+232x^45+279x^46+418x^47+512x^48+412x^49+469x^50+416x^51+258x^52+186x^53+135x^54+114x^55+66x^56+68x^57+32x^58+16x^59+22x^60+2x^61+2x^62+1x^80

The gray image is a linear code over GF(2) with n=196, k=12 and d=82.
This code was found by Heurico 1.16 in 0.855 seconds.