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 X^2  X  X  0  1  X  X  X  1  1  0 X^2  0 X^2  1  0  X  0  X  1  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  X  X  0  0  0 X^2 X^2+X X^2+X X^2 X^2+X  X  0 X^2+X  0  X  X X^2  0  X X^2  0  X  X  0  0 X^2  X X^2 X^2  0 X^2+X  X  0  0  X  0
 0  0  X  0  X  X X^2+X  0  0  0  X  X  X  0 X^2 X^2+X  X  0 X^2 X^2  0  0 X^2+X X^2 X^2  X X^2+X  X X^2+X  X  0  0 X^2+X X^2  0  X  0  0  0 X^2+X  X X^2  X X^2 X^2 X^2 X^2  0 X^2
 0  0  0  X  X  0 X^2+X  X X^2  X X^2  0  X X^2 X^2+X  X X^2 X^2  X X^2+X X^2  X  0  X  0 X^2+X X^2+X  0  0  0  X  0 X^2+X  X X^2+X X^2  X  X  X X^2+X X^2+X X^2+X X^2 X^2+X  0  X X^2 X^2+X  X
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 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  0  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0 X^2  0 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+155x^40+4x^41+326x^42+68x^43+655x^44+204x^45+826x^46+436x^47+1187x^48+612x^49+1088x^50+460x^51+827x^52+196x^53+552x^54+60x^55+313x^56+8x^57+138x^58+53x^60+14x^62+8x^64+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 3.98 seconds.