The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  1 X+2  0  1  2  1  2  1 X+2  1  1 X+2  1  1  0  2 X+2  1  1  X  1  X X+2  X  0  2  1  0 X+2  0  1  X  1  1  2 X+2  2  1  0  1  1  1  0 X+2  1  1  1  1
 0  1  0  0  0  0  0  0  0  2  2  2  2  0  0  3  1  1  1 X+3  1 X+1 X+3  X X+1  1  1  1  X  3 X+2  1  3  1 X+2 X+2  1 X+2 X+3  1  1  1 X+2  1  0  1  X  1  1 X+1  X X+1  2 X+3  1  1  1  0 X+1  0
 0  0  1  0  0  2  1  3  1  X  0 X+1 X+3  1  1  3 X+1  0  1 X+3  X  0  X  X  1 X+1 X+1  3  1 X+2 X+1  2 X+3  1 X+2  1  0  1  0  1 X+1 X+1  0 X+1 X+3  3  1 X+1  X X+1  1  1  X  X X+3  0  1  2 X+2  0
 0  0  0  1  0  3  1  2  3  0 X+1  X  3  0 X+3  1  3 X+2  X  2 X+3  1  1  1 X+1  0 X+2  1  X  X  2  3 X+3  0  1  1  2  0  X  X X+1  0  3 X+3  X  0 X+1 X+2 X+2  0  3  1 X+2  2 X+2 X+3  2  1  2 X+2
 0  0  0  0  1  1  2  3  3 X+1  X  0  3 X+3  X X+3 X+3  2 X+3  2  0 X+1 X+2 X+3  X  1  0  2  3 X+1 X+2  3 X+1  X  3  0 X+3  0 X+2  1 X+2  X X+2  3  1  2 X+1 X+1  X X+3  2 X+2  3  0  3  2 X+2 X+2  3  X

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+90x^51+458x^52+848x^53+1198x^54+1880x^55+2012x^56+2654x^57+2574x^58+3136x^59+2978x^60+3484x^61+2592x^62+2788x^63+1879x^64+1514x^65+1130x^66+726x^67+400x^68+226x^69+118x^70+52x^71+16x^72+8x^73+4x^74+2x^77

The gray image is a code over GF(2) with n=240, k=15 and d=102.
This code was found by Heurico 1.13 in 14.3 seconds.