The generator matrix

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

generates a code of length 49 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+112x^41+747x^42+2284x^43+5950x^44+11294x^45+20864x^46+29072x^47+40299x^48+39670x^49+41702x^50+29900x^51+20750x^52+10646x^53+5504x^54+2136x^55+796x^56+282x^57+71x^58+32x^59+12x^60+12x^61+8x^62

The gray image is a linear code over GF(2) with n=392, k=18 and d=164.
This code was found by Heurico 1.16 in 371 seconds.