The generator matrix

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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 44.

Homogenous weight enumerator: w(x)=1x^0+196x^44+128x^45+176x^46+8x^48+2x^56+1x^64

The gray image is a linear code over GF(2) with n=360, k=9 and d=176.
This code was found by Heurico 1.16 in 0.047 seconds.