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  0  X  X  1  1  0  0  1  1  X  0  1 X^2  1  X  1 X^2  X  X  X  1  X  1  1  X  X  1
 0  X  0  X  0  0  X X^2+X  0 X^2 X^2+X  X  0  X  X X^2 X^2 X^2+X  0  X X^2+X  X  X X^2+X X^2+X  0 X^2  0  0  X  X X^2 X^2 X^2+X  X  0  0  X  X X^2  X X^2+X  0 X^2+X  0 X^2 X^2+X  X  0
 0  0  X  X  0 X^2+X  X  0 X^2  X  0  X  0 X^2+X X^2  X  X X^2  0 X^2+X X^2+X X^2  0 X^2  0  X  X  X  X  X X^2+X  X  X  X X^2+X  0 X^2+X X^2+X  X  X X^2  0 X^2+X X^2 X^2+X X^2  0  X  0
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 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+46x^40+44x^41+99x^42+138x^43+208x^44+286x^45+289x^46+358x^47+381x^48+416x^49+435x^50+392x^51+290x^52+220x^53+128x^54+120x^55+82x^56+52x^57+55x^58+14x^59+14x^60+6x^61+15x^62+2x^63+2x^64+3x^66

The gray image is a linear code over GF(2) with n=196, k=12 and d=80.
This code was found by Heurico 1.16 in 0.888 seconds.