The generator matrix

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

generates a code of length 78 over Z4 who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+24x^65+87x^66+148x^67+224x^68+268x^69+333x^70+354x^71+349x^72+384x^73+406x^74+460x^75+459x^76+428x^77+441x^78+458x^79+429x^80+464x^81+426x^82+360x^83+342x^84+316x^85+286x^86+202x^87+133x^88+128x^89+110x^90+56x^91+37x^92+28x^93+19x^94+10x^95+8x^96+8x^97+3x^98+2x^100+1x^118

The gray image is a code over GF(2) with n=156, k=13 and d=65.
This code was found by Heurico 1.10 in 4.57 seconds.