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

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+119x^42+118x^43+187x^44+236x^45+310x^46+386x^47+428x^48+480x^49+460x^50+392x^51+252x^52+196x^53+152x^54+100x^55+74x^56+44x^57+36x^58+26x^59+17x^60+8x^61+10x^62+2x^63+1x^64+1x^74

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 1.79 seconds.