The generator matrix

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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+69x^36+246x^37+532x^38+856x^39+1344x^40+1888x^41+2581x^42+3162x^43+3517x^44+4116x^45+3861x^46+3202x^47+2638x^48+1844x^49+1327x^50+786x^51+392x^52+206x^53+75x^54+54x^55+37x^56+20x^57+8x^58+4x^59+2x^60

The gray image is a linear code over GF(2) with n=180, k=15 and d=72.
This code was found by Heurico 1.16 in 27.6 seconds.