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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+185x^42+292x^44+256x^45+631x^46+256x^47+243x^48+135x^50+39x^52+9x^54+1x^84

The gray image is a linear code over GF(2) with n=368, k=11 and d=168.
This code was found by Heurico 1.16 in 3.39 seconds.