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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X
 0 X^3  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3
 0  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0
 0  0  0 X^3  0  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0  0
 0  0  0  0 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0
 0  0  0  0  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  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+32x^44+102x^48+768x^49+64x^50+48x^52+8x^56+1x^96

The gray image is a linear code over GF(2) with n=392, k=10 and d=176.
This code was found by Heurico 1.16 in 0.078 seconds.