The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+72x^57+124x^58+120x^59+870x^60+56x^61+540x^62+8x^63+32x^64+64x^65+96x^66+64x^67+1x^120

The gray image is a linear code over GF(2) with n=488, k=11 and d=228.
This code was found by Heurico 1.16 in 0.297 seconds.