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  X  1  1  1  1  X  1  1
 0 X^3  0  0  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3
 0  0 X^3  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0
 0  0  0 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0
 0  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  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  0 X^3  0 X^3  0  0  0  0 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3
 0  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+21x^40+29x^42+32x^43+19x^44+832x^45+21x^46+32x^47+14x^48+7x^50+9x^52+6x^54+1x^86

The gray image is a linear code over GF(2) with n=360, k=10 and d=160.
This code was found by Heurico 1.16 in 0.062 seconds.