The generator matrix

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

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+204x^76+734x^77+1386x^78+1458x^79+1984x^80+2004x^81+1894x^82+1686x^83+1562x^84+1108x^85+993x^86+528x^87+416x^88+168x^89+92x^90+78x^91+31x^92+30x^93+9x^94+10x^95+1x^96+4x^97+1x^98+1x^100+1x^106

The gray image is a code over GF(2) with n=656, k=14 and d=304.
This code was found by Heurico 1.16 in 3.67 seconds.