The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0 X^2+X  1  1  0  1  1 X^2+X  1  0  1  1  1  1 X^2+X  1  1  1  0  1  1  1 X^2 X^2+X  1  0  1  1  1  1  1  1  X  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X  1 X^2+1 X^2+X X^2+1  0  1 X^2+X X+1  0  1 X^2+1 X^2+1  X  1  1 X^2  1 X^2  0 X^2+1 X^2+X  0 X+1  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0 X^2  0  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0
 0  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  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+35x^40+95x^42+56x^43+245x^44+208x^45+318x^46+456x^47+316x^48+608x^49+391x^50+456x^51+304x^52+208x^53+197x^54+56x^55+100x^56+17x^58+17x^60+4x^62+3x^64+1x^66+2x^68+1x^70+1x^72

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 0.634 seconds.