The generator matrix

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

generates a code of length 62 over Z4 who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+126x^54+280x^56+318x^58+297x^60+218x^62+214x^64+172x^66+165x^68+124x^70+71x^72+34x^74+26x^76+2x^80

The gray image is a code over GF(2) with n=124, k=11 and d=54.
This code was found by Heurico 1.16 in 0.563 seconds.