The generator matrix

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

generates a code of length 77 over Z4 who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+55x^68+88x^69+117x^70+148x^71+118x^72+140x^73+161x^74+134x^75+135x^76+134x^77+85x^78+82x^79+89x^80+78x^81+81x^82+78x^83+63x^84+68x^85+35x^86+26x^87+40x^88+28x^89+25x^90+4x^91+7x^92+6x^93+7x^94+8x^95+4x^96+2x^97+1x^98

The gray image is a code over GF(2) with n=154, k=11 and d=68.
This code was found by Heurico 1.10 in 0.25 seconds.