The generator matrix

 1  0  0  1  1  1  0  1  1  2  1  1  2  2  1  1  0  1  0  2  1  1  1  2  2  1  1  2  1  1  2  2  2  1  0  1  0  1  0  1  1  1  0  0  0  1  2  1  1  1  2  1  0  2  2  2  1  1  1  1
 0  1  0  0  1  1  1  0  2  0  1  3  1  1  2  2  0  3  1  1  3  2  3  1  1  2  3  0  0  3  1  1  2  2  1  1  1  3  2  0  2  0  2  1  1  1  0  2  1  2  1  0  1  0  1  1  2  1  2  3
 0  0  1  1  1  0  1  2  3  1  0  3  2  1  0  3  1  3  2  3  0  2  3  3  0  1  0  1  3  0  0  2  1  1  3  0  0  3  1  1  3  0  1  2  3  3  1  1  3  3  3  3  3  1  3  1  0  3  1  2
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  2  0  2  2  2  2  2  0  0  2  0  2  2  0  0  2  2  0  2  0  2  2  2  0  2  0  0  0  2  2  0  2  2  2  2  0  2  0  0  0
 0  0  0  0  2  0  0  2  2  0  2  0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  2  0  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  0  2  2  0  0  0  0  2  2  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  2  2  0  2  0  0  2  2  0  0  2  2  2  2  2  2  2  0  2  0  2  2  0  0  2  0  0
 0  0  0  0  0  0  2  2  0  2  2  0  2  0  2  2  2  2  0  2  0  2  2  2  2  2  2  0  0  0  2  0  0  0  0  0  0  2  2  2  0  2  0  0  0  0  0  2  2  2  2  0  2  2  0  0  0  2  2  0

generates a code of length 60 over Z4 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+54x^53+94x^54+78x^55+53x^56+78x^57+136x^58+76x^59+32x^60+64x^61+70x^62+50x^63+25x^64+36x^65+45x^66+34x^67+8x^68+18x^69+34x^70+16x^71+9x^72+6x^73+2x^74+2x^75+2x^78+1x^82

The gray image is a code over GF(2) with n=120, k=10 and d=53.
This code was found by Heurico 1.16 in 0.365 seconds.