The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  1 X^2  0  X  1  X  1  0  1 X^2  1  0  1 X^2  1  1  1  1  1  X  0  1  0  0  X X^2  1 X^2  1  1  0  X  X  0 X^2+X  1  X  0  1
 0  1  0  1  0  1  1  X  1  X X^2+X+1  1 X^2+X  1  1  1 X^2  1  X X^2+X X^2+1 X^2  1  1  0 X^2+1 X^2+X X^2+X X+1  1  1  0 X^2  1  1  1 X+1  1  0 X^2+1  X  1  0  1  1 X+1  1  1 X^2
 0  0  1  1  1  0  1 X+1  1  X  X  X  1 X+1  1 X^2+1  0 X^2 X^2+1  1  0  1 X^2+1  1  0 X^2+X X^2 X+1 X^2+X+1  X X^2  X  1 X^2+1  1  1  1 X^2+X+1  X X+1  1 X^2+X+1  X  0 X+1  X  0 X+1  0
 0  0  0  X  0  0  0  0  0  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 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  X X^2  X  X  X  X  0 X^2+X X^2  X  X  X  0  X
 0  0  0  0  X  0  0  0 X^2 X^2+X  X X^2+X X^2+X  X  X  0 X^2  X  0  X  X X^2 X^2  X X^2 X^2+X X^2 X^2 X^2+X  0  X X^2+X X^2 X^2  X  0  0 X^2+X  X X^2+X  0  0  0  X  0  X  X X^2+X X^2+X
 0  0  0  0  0  X X^2+X X^2+X  0  X X^2 X^2+X X^2+X  0 X^2+X X^2 X^2+X  0 X^2  0  X  X  X X^2+X X^2+X X^2+X  0  X  0 X^2  X X^2 X^2+X  0 X^2  X  0 X^2+X  X X^2  0 X^2+X X^2+X X^2 X^2 X^2  X  0 X^2+X

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+154x^40+224x^41+808x^42+724x^43+1733x^44+1720x^45+2698x^46+2640x^47+3670x^48+3548x^49+4004x^50+2976x^51+2987x^52+1636x^53+1466x^54+640x^55+629x^56+164x^57+176x^58+60x^59+72x^60+4x^61+32x^62+2x^64

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 31.9 seconds.