The generator matrix

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

generates a code of length 40 over Z2[X]/(X^4) who´s minimum homogenous weight is 33.

Homogenous weight enumerator: w(x)=1x^0+248x^33+1424x^34+4266x^35+9955x^36+17616x^37+31351x^38+41096x^39+49019x^40+42372x^41+32027x^42+17942x^43+9255x^44+3452x^45+1493x^46+470x^47+120x^48+20x^49+9x^50+2x^52+4x^53+2x^55

The gray image is a linear code over GF(2) with n=320, k=18 and d=132.
This code was found by Heurico 1.16 in 286 seconds.