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

generates a code of length 50 over Z2[X]/(X^3) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+88x^41+155x^42+178x^43+244x^44+288x^45+427x^46+604x^47+682x^48+920x^49+1036x^50+906x^51+786x^52+562x^53+428x^54+278x^55+164x^56+162x^57+113x^58+76x^59+42x^60+22x^61+17x^62+6x^63+6x^65+1x^80

The gray image is a linear code over GF(2) with n=200, k=13 and d=82.
This code was found by Heurico 1.16 in 79.4 seconds.