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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+124x^59+106x^60+116x^61+60x^62+36x^63+19x^64+44x^65+2x^66+2x^68+2x^74

The gray image is a linear code over GF(2) with n=488, k=9 and d=236.
This code was found by Heurico 1.16 in 1.44 seconds.