The generator matrix

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

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+103x^44+24x^45+90x^46+192x^47+351x^48+592x^49+322x^50+192x^51+67x^52+24x^53+30x^54+40x^56+6x^58+13x^60+1x^84

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 0.171 seconds.