The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+264x^72+72x^73+807x^74+152x^75+745x^76+112x^77+791x^78+80x^79+687x^80+72x^81+189x^82+24x^83+91x^84+5x^86+3x^96+1x^104

The gray image is a code over GF(2) with n=616, k=12 and d=288.
This code was found by Heurico 1.16 in 11.5 seconds.