The generator matrix

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

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+35x^40+66x^41+120x^42+174x^43+434x^44+586x^45+495x^46+736x^47+1070x^48+968x^49+803x^50+836x^51+633x^52+464x^53+314x^54+160x^55+103x^56+86x^57+50x^58+14x^59+20x^60+6x^61+7x^62+7x^64+3x^66+1x^68

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 2.75 seconds.