The generator matrix

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

generates a code of length 46 over Z2[X]/(X^3) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+72x^39+293x^40+448x^41+510x^42+648x^43+790x^44+922x^45+956x^46+872x^47+793x^48+678x^49+452x^50+300x^51+218x^52+118x^53+60x^54+24x^55+17x^56+10x^57+6x^58+4x^59

The gray image is a linear code over GF(2) with n=184, k=13 and d=78.
This code was found by Heurico 1.16 in 2.2 seconds.