The generator matrix

 1  0  1  1  1  0  1  1  X  1 X^2+X  1  1  1  0  1  1 X^2  X  1  1 X^2+X  1  0  1  1  1  1  1  1  1  X  X  1 X^2+X  1  1  0  1  0  1  0  X  1  1 X^2  1  1  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+X  1 X^2+1  0 X+1  1 X^2 X^2+X+1  1  1 X^2+X  1  1  X  1 X^2+1  0 X^2+X X^2+X  1 X^2+1  0  1  1 X^2+1  1 X^2+X+1 X^2  1 X^2  1  0  1 X^2+X X^2+X X^2+1  1  0  0 X+1
 0  0  X X^2+X  0 X^2+X  X X^2+X  X  0 X^2  0 X^2  0  0  X X^2+X X^2+X  X X^2  X X^2  X  0  0  0  0  0  X  0 X^2 X^2+X X^2+X X^2  0 X^2+X  X X^2  X X^2  0  0  X X^2+X  X  X  0 X^2  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0 X^2  0  0  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0 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 40.

Homogenous weight enumerator: w(x)=1x^0+208x^40+478x^42+1339x^44+2320x^46+3920x^48+3720x^50+2453x^52+1292x^54+436x^56+122x^58+73x^60+4x^62+11x^64+7x^68

The gray image is a linear code over GF(2) with n=196, k=14 and d=80.
This code was found by Heurico 1.16 in 10.2 seconds.