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

generates a code of length 49 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+62x^38+74x^39+207x^40+250x^41+322x^42+354x^43+590x^44+796x^45+1054x^46+1580x^47+1841x^48+2044x^49+1955x^50+1644x^51+1028x^52+800x^53+528x^54+362x^55+345x^56+186x^57+136x^58+82x^59+78x^60+20x^61+35x^62+6x^64+3x^66+1x^78

The gray image is a linear code over GF(2) with n=196, k=14 and d=76.
This code was found by Heurico 1.16 in 13.4 seconds.