The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  X X^2+X  1 X^2  X  1  1  X  1  1  X  1  1  1  X  1  X  1  1 X^2+X  1  1  1  1 X^2  1 X^2+X  1  1 X^2+X  1  1  0  1  X  1  1  1
 0  1  0  0  0  1  1  1 X^2+X+1 X^2+1  X  1 X^2+X X^2  1  X X^2+X  1  1 X^2+X  0  1 X^2+X+1 X^2+1  0  1  1 X^2 X^2 X^2+X+1  1  0 X^2+1 X^2+X X^2+X X^2+X  1  1 X^2 X^2+1  1  1 X+1  1 X^2+X X^2 X+1  X  0
 0  0  1  0  1  1  0  1 X^2+1 X^2+X  X X^2+1  1  1  0 X^2  1 X^2+X+1  X X^2+X+1  X  1  0  0  0 X^2 X^2+1  1 X^2+X+1 X+1 X^2+X+1 X+1 X^2+X+1  X X^2  1  0 X^2+X+1 X^2+X  X X^2+1 X^2+1  1 X^2  1  1 X^2+X+1 X^2+1  0
 0  0  0  1  1  0  1 X^2+1 X^2+X+1 X^2 X^2+X+1  0 X+1 X^2  1  1  1 X^2+1 X^2+X  0 X^2+X  X  1 X^2 X^2+X+1 X^2+1 X^2+X  1 X^2+1  1 X^2  0 X+1  X X^2+1  0  X X+1 X^2+X X^2+X+1 X^2+1 X^2  1 X^2+1 X^2+X X^2+X+1 X^2+X+1  0  0
 0  0  0  0 X^2  0  0 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 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0  0
 0  0  0  0  0 X^2  0  0  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  0 X^2  0 X^2 X^2 X^2 X^2  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  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 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+84x^40+286x^41+768x^42+966x^43+1580x^44+1908x^45+2554x^46+2782x^47+3683x^48+3326x^49+3734x^50+3116x^51+2761x^52+1804x^53+1461x^54+872x^55+547x^56+218x^57+173x^58+70x^59+47x^60+8x^61+13x^62+2x^63+1x^64+2x^65+1x^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 28.5 seconds.