The generator matrix

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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+282x^39+1504x^40+3532x^41+4604x^42+8266x^43+9050x^44+11266x^45+8954x^46+8390x^47+4729x^48+3056x^49+1168x^50+488x^51+170x^52+34x^53+26x^54+12x^55+2x^56+2x^59

The gray image is a linear code over GF(2) with n=360, k=16 and d=156.
This code was found by Heurico 1.16 in 28 seconds.