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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+20x^57+88x^58+32x^59+24x^60+60x^62+7x^64+8x^65+8x^66+4x^70+4x^73

The gray image is a code over GF(2) with n=240, k=8 and d=114.
This code was found by Heurico 1.16 in 8.46 seconds.