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

generates a code of length 57 over Z2[X]/(X^4) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+236x^49+1317x^50+3518x^51+7347x^52+12458x^53+21277x^54+27994x^55+37004x^56+38268x^57+38608x^58+28856x^59+21735x^60+12072x^61+6283x^62+2984x^63+1427x^64+522x^65+129x^66+50x^67+32x^68+10x^69+2x^70+6x^71+6x^72+2x^73

The gray image is a linear code over GF(2) with n=456, k=18 and d=196.
This code was found by Heurico 1.16 in 454 seconds.