The generator matrix

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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+143x^60+282x^62+334x^64+262x^66+257x^68+164x^70+185x^72+136x^74+111x^76+94x^78+47x^80+18x^82+9x^84+4x^86+1x^88

The gray image is a code over GF(2) with n=136, k=11 and d=60.
This code was found by Heurico 1.16 in 0.789 seconds.