The generator matrix

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

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+110x^45+1078x^46+2908x^47+6622x^48+12160x^49+20624x^50+29096x^51+38035x^52+40114x^53+38257x^54+30132x^55+21494x^56+11536x^57+5812x^58+2572x^59+1039x^60+340x^61+107x^62+40x^63+41x^64+12x^65+10x^66+4x^67

The gray image is a linear code over GF(2) with n=424, k=18 and d=180.
This code was found by Heurico 1.16 in 413 seconds.