The generator matrix

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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+204x^62+109x^64+272x^66+66x^68+132x^70+37x^72+86x^74+20x^76+46x^78+12x^80+26x^82+10x^84+2x^86+1x^88

The gray image is a code over GF(2) with n=136, k=10 and d=62.
This code was found by Heurico 1.16 in 51.8 seconds.