The generator matrix

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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+228x^41+746x^42+1550x^43+2010x^44+2662x^45+2374x^46+2670x^47+1769x^48+1202x^49+608x^50+300x^51+154x^52+82x^53+14x^54+6x^55+2x^56+2x^57+2x^58+2x^59

The gray image is a linear code over GF(2) with n=368, k=14 and d=164.
This code was found by Heurico 1.16 in 2.34 seconds.