The generator matrix

 1  0  0  0  0  1  1  1  1 X^2+X  1  0  X  1  1 X^2 X^2+X X^2  X X^2  1  0  1  1 X^2  1  1  1 X^2  1  X X^2+X X^2+X  1  1  1  1  1  1 X^2  1  X  X  1  X X^2+X  1  0  1
 0  1  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2  0  X  X  1  1  1  1  1  1 X^2+1 X+1  1  1  1  1  1 X^2+X+1 X^2+X  1 X^2+X X^2  X  X X^2+1  1  X  X X+1 X^2+X  1  X  1  X  0  1  0
 0  0  1  0  0  0 X^2+1 X+1 X^2  1 X^2+1  1  1 X+1 X^2 X^2+X X^2+X  0 X+1 X^2+X X^2 X+1  1 X^2+X+1 X^2+X+1  X  1  X X^2+1 X+1 X^2 X+1  0 X^2+X X^2+1 X+1  0 X+1  X  1 X+1  0  0 X^2+X+1  X  1 X^2+1 X^2+X+1  0
 0  0  0  1  0  1  1  X X^2+X  X X^2 X^2+1  1 X^2+X+1 X^2+X+1  1 X^2+X+1 X^2+X+1 X^2  0 X^2+1 X^2+X  0 X+1 X^2+X+1  0  0  X X^2+X+1  1  X X^2  1  0 X^2+X X+1 X^2+1 X^2 X^2+X+1 X^2+X+1 X^2+X+1  1 X^2+X X^2 X^2  1 X^2 X+1  0
 0  0  0  0  1  1 X^2  0 X^2+X+1 X^2+X+1  1 X^2+1  0 X+1  X X^2+1  X X^2+1 X^2 X+1 X+1 X^2+1  0  X X^2+X+1  X X^2+X+1 X^2+1 X^2+X X+1  1 X^2+X X^2+1 X^2+1 X^2+1 X^2+1  0 X^2  1 X^2+X+1 X^2 X+1 X^2+X X^2 X+1 X^2+1  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 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 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+218x^40+640x^41+1135x^42+2080x^43+2716x^44+4056x^45+4919x^46+6336x^47+6873x^48+7356x^49+6866x^50+6592x^51+5086x^52+4356x^53+2640x^54+1732x^55+984x^56+500x^57+235x^58+120x^59+50x^60+20x^61+13x^62+4x^63+8x^64

The gray image is a linear code over GF(2) with n=196, k=16 and d=80.
This code was found by Heurico 1.13 in 35.9 seconds.