The generator matrix

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

generates a code of length 78 over Z4 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+33x^62+102x^63+174x^64+308x^65+460x^66+590x^67+768x^68+842x^69+923x^70+1108x^71+1282x^72+1448x^73+1642x^74+1868x^75+1869x^76+1882x^77+1997x^78+1906x^79+1873x^80+1844x^81+1796x^82+1608x^83+1408x^84+1170x^85+900x^86+848x^87+592x^88+444x^89+349x^90+252x^91+180x^92+106x^93+74x^94+36x^95+37x^96+20x^97+16x^98+2x^99+6x^100+1x^102+1x^106+1x^108+1x^112

The gray image is a code over GF(2) with n=156, k=15 and d=62.
This code was found by Heurico 1.10 in 131 seconds.