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

generates a code of length 81 over Z4 who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+88x^69+178x^70+232x^71+263x^72+304x^73+361x^74+390x^75+414x^76+418x^77+438x^78+416x^79+422x^80+476x^81+441x^82+422x^83+451x^84+390x^85+382x^86+350x^87+275x^88+264x^89+227x^90+174x^91+132x^92+94x^93+64x^94+56x^95+23x^96+12x^97+18x^98+6x^99+3x^100+2x^101+2x^102+2x^103+1x^114

The gray image is a code over GF(2) with n=162, k=13 and d=69.
This code was found by Heurico 1.10 in 5.21 seconds.