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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+67x^54+65x^56+235x^58+235x^60+256x^61+33x^62+34x^64+49x^66+48x^68+1x^116

The gray image is a code over GF(2) with n=240, k=10 and d=108.
This code was found by Heurico 1.16 in 0.209 seconds.