The generator matrix

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

generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+562x^78+288x^79+678x^80+304x^81+600x^82+320x^83+617x^84+192x^85+364x^86+32x^87+72x^88+16x^89+12x^90+21x^92+10x^94+4x^98+1x^104+2x^108

The gray image is a code over GF(2) with n=656, k=12 and d=312.
This code was found by Heurico 1.16 in 97.2 seconds.