The generator matrix

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

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+204x^73+190x^74+152x^75+192x^76+568x^77+192x^78+152x^79+190x^80+204x^81+1x^90+1x^106+1x^112

The gray image is a code over GF(2) with n=616, k=11 and d=292.
This code was found by Heurico 1.16 in 0.344 seconds.