The generator matrix

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

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+145x^40+4x^41+384x^42+32x^43+591x^44+196x^45+770x^46+520x^47+1179x^48+556x^49+1226x^50+496x^51+820x^52+204x^53+492x^54+40x^55+346x^56+116x^58+53x^60+18x^62+2x^66+1x^72

The gray image is a linear code over GF(2) with n=196, k=13 and d=80.
This code was found by Heurico 1.16 in 3.98 seconds.