The generator matrix

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

generates a code of length 41 over Z2[X]/(X^4) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+164x^35+1192x^36+2478x^37+5403x^38+7470x^39+10768x^40+10426x^41+11149x^42+7776x^43+5012x^44+2110x^45+1157x^46+270x^47+107x^48+24x^49+19x^50+8x^52+2x^57

The gray image is a linear code over GF(2) with n=328, k=16 and d=140.
This code was found by Heurico 1.16 in 20 seconds.