The generator matrix

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

generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+230x^76+28x^77+252x^78+144x^79+493x^80+588x^81+746x^82+608x^83+437x^84+148x^85+154x^86+16x^87+132x^88+4x^89+62x^90+31x^92+2x^94+14x^96+5x^100+1x^140

The gray image is a code over GF(2) with n=656, k=12 and d=304.
This code was found by Heurico 1.16 in 5.14 seconds.