The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+65x^76+130x^77+153x^78+234x^79+262x^80+270x^81+380x^82+354x^83+444x^84+426x^85+425x^86+458x^87+401x^88+428x^89+429x^90+408x^91+350x^92+422x^93+351x^94+360x^95+304x^96+262x^97+193x^98+162x^99+160x^100+94x^101+89x^102+66x^103+51x^104+16x^105+19x^106+4x^107+5x^108+4x^110+2x^111+5x^112+3x^114+2x^118

The gray image is a code over GF(2) with n=178, k=13 and d=76.
This code was found by Heurico 1.16 in 15.6 seconds.