The generator matrix

 1  0  0  1  1  1  X X+2  1  1  1 X^2+X+2  1  0  1  1  2  1  X X^2+X+2  1 X^2+2  1  1  1 X+2 X^2+2  X  1  1  1 X^2+X+2  2 X^2  1  0  1  2  1  1  1 X^2  1  1  1  2  1  1  1  X X+2 X^2+X  1  X X^2+X+2  1  1 X+2  1  0 X+2  1  1 X^2+X  1 X^2+2  1  0  1  1  1  1  1  1  1  1  1  1  1 X^2 X^2+X+2 X^2+X+2  1  1
 0  1  0  0 X^2+1 X+1  1  2  0  2 X^2+X+3  1  1  1 X^2+2 X^2+X+1  1 X+2  0  1 X+3  1 X^2+1 X^2+1  X X^2+X+2 X^2+X  1 X^2+X+2 X^2+2  X  1  1  1 X^2+X+3  1 X^2+2 X^2+X X+1  X X^2+1  1 X+3 X^2+X+3 X^2+1  0 X^2+3  X X^2+X+1  1  1  X X+2  0  1  X X^2+X  1 X^2+1  1  1  3 X^2  1 X^2+X  1  1 X^2+2 X+3 X^2+1  0 X^2+2  2 X^2+X+2  1 X+3  0 X^2 X^2+2  1  1 X^2+X+2 X^2+X  2
 0  0  1  1  1  0 X^2+1  1  X X^2+X+3  1 X^2+X X^2+X X^2+X+1 X^2+X+3 X+2  1 X^2  1 X^2+X+2 X^2+3  2  X X^2+X+3 X+3  1  1 X+3 X^2+3 X^2+X+2 X^2+X+2 X^2+2 X+1 X^2+X+2 X+1 X^2+X+3 X^2  1 X^2 X+3 X+3 X+2 X^2+X+2 X+1  0  1  2 X^2+1  2  1 X^2+X+3  1  2  1  2  1 X+3 X^2+3 X+2 X^2+1 X^2  3  0 X^2+X+2 X^2+X X^2+3 X+1  1  X X+2 X^2+1 X^2+3 X+3 X+2  3 X+3  1 X^2+2 X^2+2 X^2+X+1  X  1 X^2+X  0
 0  0  0  X X+2  2 X+2 X+2 X+2  X X^2+2 X^2+X X+2 X^2+2 X^2 X^2+X+2 X+2 X^2  2  0 X+2 X^2+X  2  0 X^2+2 X^2+X+2  0 X^2+2 X^2+2  2 X^2+X  2  2 X^2+2 X+2 X^2+X+2 X+2 X^2+X X^2+X X^2+X+2 X+2 X^2+X+2 X^2  0 X^2+X X^2+X  2  0 X^2  0 X+2 X^2  0 X^2+X+2 X^2+X+2 X^2+X+2  0 X^2+2 X^2+2 X^2  X X^2+2 X^2+2 X^2+2 X^2+X  X X^2+X+2 X^2+X+2  X X^2+X X^2+2 X^2+X+2  2  0  0 X^2+X  2  2 X^2+X X^2+X+2 X^2 X^2  2 X^2+2

generates a code of length 84 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+102x^77+808x^78+1604x^79+2105x^80+2938x^81+3712x^82+3578x^83+4213x^84+3442x^85+3230x^86+2476x^87+1760x^88+1174x^89+749x^90+400x^91+239x^92+104x^93+56x^94+32x^95+14x^96+16x^97+5x^98+6x^99+2x^100+2x^104

The gray image is a code over GF(2) with n=672, k=15 and d=308.
This code was found by Heurico 1.16 in 13.4 seconds.