The generator matrix

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

generates a code of length 77 over Z4 who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+90x^67+153x^68+196x^69+210x^70+234x^71+253x^72+218x^73+241x^74+236x^75+253x^76+228x^77+225x^78+210x^79+171x^80+174x^81+143x^82+130x^83+157x^84+146x^85+119x^86+96x^87+51x^88+56x^89+48x^90+22x^91+17x^92+6x^93+6x^94+4x^95+2x^99

The gray image is a code over GF(2) with n=154, k=12 and d=67.
This code was found by Heurico 1.09 in 114 seconds.