The generator matrix

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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+138x^39+1065x^40+2650x^41+6081x^42+9156x^43+15910x^44+18872x^45+22861x^46+19120x^47+16884x^48+9116x^49+5502x^50+2252x^51+914x^52+364x^53+143x^54+22x^55+8x^56+2x^57+3x^58+2x^60+4x^61+2x^62

The gray image is a linear code over GF(2) with n=368, k=17 and d=156.
This code was found by Heurico 1.16 in 90 seconds.