The generator matrix

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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+199x^42+410x^43+330x^44+334x^45+247x^46+286x^47+120x^48+50x^49+48x^50+8x^51+12x^52+1x^54+1x^56+1x^66

The gray image is a linear code over GF(2) with n=360, k=11 and d=168.
This code was found by Heurico 1.16 in 0.468 seconds.