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

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+69x^54+82x^56+64x^57+88x^58+384x^59+728x^60+320x^61+178x^62+36x^64+48x^66+48x^68+1x^70+1x^112

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 0.297 seconds.