The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+133x^78+236x^79+615x^80+360x^81+653x^82+380x^83+512x^84+336x^85+414x^86+196x^87+139x^88+8x^89+71x^90+20x^91+5x^92+7x^94+6x^96+2x^98+1x^116+1x^120

The gray image is a code over GF(2) with n=664, k=12 and d=312.
This code was found by Heurico 1.16 in 0.875 seconds.