The generator matrix

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

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+45x^40+92x^41+203x^42+284x^43+597x^44+418x^45+880x^46+394x^47+598x^48+256x^49+187x^50+66x^51+34x^52+10x^53+7x^54+6x^55+2x^56+8x^57+2x^59+3x^60+2x^62+1x^70

The gray image is a linear code over GF(2) with n=368, k=12 and d=160.
This code was found by Heurico 1.16 in 0.312 seconds.