The generator matrix

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

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+80x^57+285x^58+356x^59+542x^60+476x^61+705x^62+454x^63+490x^64+344x^65+233x^66+68x^67+35x^68+10x^69+6x^70+2x^71+3x^72+2x^77+2x^78+1x^84+1x^94

The gray image is a linear code over GF(2) with n=496, k=12 and d=228.
This code was found by Heurico 1.16 in 0.344 seconds.