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  X  X  X  X  X  X  X  1  1  1  1  1  1  X  X  X  X 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2  X  X  1  X  1  X  1  1  1  1  1  1  1  1
 0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0 2X  0 2X  0 2X 2X  0  0  0 2X  0 2X
 0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0  0 2X 2X 2X 2X
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X  0  0  0

generates a code of length 60 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+28x^59+85x^60+7x^64+4x^67+2x^68+1x^76

The gray image is a code over GF(2) with n=480, k=7 and d=236.
This code was found by Heurico 1.16 in 0.11 seconds.