The generator matrix

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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+97x^40+686x^41+1685x^42+2452x^43+3981x^44+4764x^45+5406x^46+4938x^47+4182x^48+2408x^49+1250x^50+506x^51+211x^52+108x^53+70x^54+6x^55+8x^56+2x^57+5x^58+2x^59

The gray image is a linear code over GF(2) with n=368, k=15 and d=160.
This code was found by Heurico 1.16 in 8.75 seconds.