The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+180x^60+12x^62+48x^64+12x^66+2x^68+1x^72

The gray image is a linear code over GF(2) with n=488, k=8 and d=240.
This code was found by Heurico 1.16 in 3.45 seconds.