The generator matrix

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

generates a code of length 48 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+82x^40+788x^41+2400x^42+5542x^43+10756x^44+20132x^45+29549x^46+41368x^47+41248x^48+40842x^49+29760x^50+20202x^51+11028x^52+5370x^53+1855x^54+828x^55+267x^56+82x^57+18x^58+12x^59+10x^60+2x^61+2x^62

The gray image is a linear code over GF(2) with n=384, k=18 and d=160.
This code was found by Heurico 1.16 in 362 seconds.