The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  1  1  1  1 X^2  1  1  0  1  X X^2  X X^2  X  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2  0 X^3 X^3+X^2 X^2 X^3+X^2 X^2  0  0  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2
 0  0 X^3  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3
 0  0  0  0  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 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+68x^40+104x^42+64x^43+252x^44+448x^45+176x^46+448x^47+269x^48+64x^49+104x^50+32x^52+11x^56+4x^60+2x^64+1x^72

The gray image is a linear code over GF(2) with n=368, k=11 and d=160.
This code was found by Heurico 1.16 in 0.141 seconds.