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

generates a code of length 50 over Z2[X]/(X^4) who´s minimum homogenous weight is 46.

Homogenous weight enumerator: w(x)=1x^0+17x^46+52x^47+33x^48+272x^49+288x^50+280x^51+24x^52+16x^53+14x^54+20x^55+6x^56+1x^94

The gray image is a linear code over GF(2) with n=400, k=10 and d=184.
This code was found by Heurico 1.16 in 0.109 seconds.