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

generates a code of length 49 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+105x^40+126x^41+164x^42+242x^43+351x^44+466x^45+539x^46+782x^47+896x^48+932x^49+914x^50+752x^51+530x^52+404x^53+330x^54+240x^55+133x^56+110x^57+89x^58+30x^59+31x^60+10x^61+11x^62+2x^63+1x^64+1x^74

The gray image is a linear code over GF(2) with n=196, k=13 and d=80.
This code was found by Heurico 1.16 in 3.69 seconds.