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

generates a code of length 60 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+50x^54+122x^56+16x^57+147x^58+368x^59+692x^60+368x^61+125x^62+16x^63+60x^64+45x^66+19x^68+17x^70+1x^72+1x^108

The gray image is a linear code over GF(2) with n=480, k=11 and d=216.
This code was found by Heurico 1.16 in 0.297 seconds.