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  X  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^3+X X^3+X^2 X^2+X X^2 X^2+X X^3+X  0 X^3+X^2+X X^3  X X^3+X^2  0 X^2+X X^3 X^3+X^2+X X^3+X X^3+X X^3+X^2 X^2 X^3 X^2+X X^3+X^2 X^3+X  0  0 X^2+X  0  X X^3+X^2 X^2 X^2+X X^3+X^2+X X^3 X^3+X  0 X^3+X^2 X^2+X X^3+X^2 X^3+X X^2+X
 0  0 X^3  0  0  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3  0  0
 0  0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0
 0  0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3
 0  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3

generates a code of length 49 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+95x^44+146x^46+96x^47+161x^48+1088x^49+132x^50+96x^51+132x^52+74x^54+26x^56+1x^92

The gray image is a linear code over GF(2) with n=392, k=11 and d=176.
This code was found by Heurico 1.16 in 0.156 seconds.