The generator matrix

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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+378x^57+1284x^58+1488x^59+2202x^60+1988x^61+2408x^62+1888x^63+1880x^64+1156x^65+755x^66+382x^67+338x^68+120x^69+76x^70+16x^71+9x^72+6x^73+3x^74+2x^75+2x^76+2x^78

The gray image is a linear code over GF(2) with n=496, k=14 and d=228.
This code was found by Heurico 1.16 in 4.58 seconds.