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

generates a code of length 60 over Z4[X]/(X^2+2) 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 code over GF(2) with n=480, k=11 and d=216.
This code was found by Heurico 1.16 in 0.282 seconds.