The generator matrix

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

generates a code of length 60 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+68x^53+154x^54+258x^55+309x^56+378x^57+402x^58+364x^59+369x^60+358x^61+362x^62+342x^63+309x^64+160x^65+88x^66+62x^67+26x^68+20x^69+16x^70+24x^71+7x^72+6x^73+2x^74+6x^75+1x^76+2x^77+2x^80

The gray image is a code over GF(2) with n=240, k=12 and d=106.
This code was found by Heurico 1.16 in 0.872 seconds.