The generator matrix

 1  0  0  0  1  1  1  0  1  X  1 X^2+X  1 X^2+X  1  1  1  0  1  X X^2  0 X^2+X  X  1  1  1 X^2  0  1  1  X  1 X^2  1  0  0  0 X^2+X  1  1  1  1  1  1  1  0  1  1
 0  1  0  0  0  1  1  1 X^2 X^2+X X^2+1  1 X^2  1  1 X^2+X X^2+X+1  1 X+1  X  1  1  X X^2 X^2+X X^2+X+1 X^2+1  1  1  0 X^2+1  1 X+1 X^2+X X^2  1  0  1  1  0  1 X^2+X+1  0 X^2+X+1 X+1 X^2+X  1  0  0
 0  0  1  0  1  1 X^2 X^2+1 X^2+X+1  1  1 X^2+X+1  X  X X^2 X^2+X+1 X^2  1 X+1 X^2+X  X  0  1  1  0 X+1 X^2 X^2+X+1  X  0 X^2+X+1 X^2+1 X^2+1  1  1  X  0 X^2+1 X^2+1 X+1  1 X^2+1 X^2+X+1  X X^2+X X^2  0  X  0
 0  0  0  1  1  0 X^2+1  1 X^2  1 X^2+1 X^2  1 X^2+X+1  0  1  1 X^2+X+1 X^2+X+1  1 X^2+X+1  X X+1  X X^2+X+1 X^2 X^2+1 X^2 X^2+X  X X+1 X^2 X^2+1 X^2+X X^2+X X^2+X+1  1 X^2+1 X+1 X^2  X  X X+1 X^2 X^2+X X^2+1 X+1  X  0
 0  0  0  0  X  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2+X X^2+X  X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X X^2+X X^2  X X^2+X X^2+X X^2+X X^2 X^2+X  X  0 X^2+X X^2  0  X X^2  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  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+69x^40+334x^41+584x^42+1186x^43+1472x^44+2080x^45+2291x^46+3318x^47+3173x^48+3690x^49+3223x^50+3164x^51+2704x^52+2180x^53+1237x^54+1092x^55+461x^56+278x^57+111x^58+66x^59+20x^60+12x^61+8x^62+6x^63+4x^64+2x^65+2x^66

The gray image is a linear code over GF(2) with n=196, k=15 and d=80.
This code was found by Heurico 1.16 in 27.7 seconds.