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

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+70x^42+72x^43+141x^44+470x^45+137x^46+60x^47+57x^48+6x^49+9x^50+1x^88

The gray image is a linear code over GF(2) with n=360, k=10 and d=168.
This code was found by Heurico 1.16 in 0.047 seconds.