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  X  X  X  X  1  1  X  X  X  1  1  1  X  X  1  0  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  X  X  0  0  X  X  X  X  X  X  X  X  0  0  X  X  X  0  X  0  0
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  0  0  X  X  X  0  0  0  X  X  0  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  X  X  X  0  X  0  0  X  X  0  0  0  X  X  X  0  X  X  0  X  0  X  0  X  X  X  X
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  0  X  0  0  X  X  X  0  X  X  X  0  X  X  0  0  0  0  0  X  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  0  X  X  0  0  0  X  X  0  X  0  X  0  X  0  X  X  X  X  0  0  X  0  0  0  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  0  X  0  X  0  X  0  X  X  X  X  X  X  X  0  0  X  X  X  0  0  0  X  X
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  0  0  X  X  X  0  0  X  X  0  X  X  0  X  X  X  X  0  X  0  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  X  X  X  X  0  0  0  X  0  X  X  X  0  X  X  X  X  X  X  X  X  X  0  0  X  X  X
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  X  0  X  X  0  0  X  0  X  X  X  0  0  X  X  X  0  X  0  0  X  0  X  0

generates a code of length 49 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+42x^38+103x^40+133x^42+191x^44+253x^46+306x^48+326x^50+259x^52+180x^54+107x^56+65x^58+42x^60+21x^62+11x^64+4x^66+3x^68+1x^76

The gray image is a linear code over GF(2) with n=98, k=11 and d=38.
This code was found by Heurico 1.16 in 0.771 seconds.