The generator matrix

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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+31x^62+140x^63+294x^64+426x^65+627x^66+864x^67+1081x^68+1430x^69+1576x^70+1886x^71+2316x^72+2492x^73+2889x^74+3206x^75+3522x^76+3724x^77+3850x^78+4072x^79+4020x^80+3952x^81+3793x^82+3418x^83+2998x^84+2766x^85+2388x^86+1910x^87+1538x^88+1148x^89+939x^90+700x^91+510x^92+344x^93+251x^94+152x^95+81x^96+94x^97+40x^98+34x^99+17x^100+8x^101+6x^104+2x^107

The gray image is a code over GF(2) with n=158, k=16 and d=62.
This code was found by Heurico 1.10 in 603 seconds.