The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+136x^73+718x^74+676x^75+591x^76+540x^77+320x^78+344x^79+295x^80+96x^81+114x^82+100x^83+108x^84+28x^85+24x^86+2x^88+2x^92+1x^100

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.