The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+192x^73+694x^74+540x^75+676x^76+492x^77+486x^78+264x^79+254x^80+116x^81+144x^82+76x^83+88x^84+40x^85+20x^86+8x^87+2x^88+2x^92+1x^96

The gray image is a code over GF(2) with n=616, k=12 and d=292.
This code was found by Heurico 1.16 in 0.344 seconds.