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

generates a code of length 60 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+34x^52+29x^54+39x^56+32x^57+36x^58+352x^59+1044x^60+352x^61+20x^62+32x^63+19x^64+18x^66+8x^68+11x^70+5x^72+10x^74+2x^76+3x^78+1x^110

The gray image is a linear code over GF(2) with n=480, k=11 and d=208.
This code was found by Heurico 1.16 in 0.234 seconds.