The generator matrix

 1  0  1  1  1 X+2  1  1 2X  1  1 3X+2  1 2X+2  1  1 3X  1  2  X  1  1  1  1  0  1 X+2  1  1  1  1 2X+2  1 3X  1  1  1  1 2X  1  1 3X+2  1  1  1  2  X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X 3X+2 2X+2 2X+2 X+2 2X+2 2X+2  2 3X+2  1  X  X 2X
 0  1 X+1 X+2  3  1 2X+1 2X  1 X+3 3X+2  1  2  1 2X+3  X  1 X+1  1  1 3X+3 2X+2 3X  1  1 3X+1  1  1  0 X+2 X+3  1 2X+3  1 2X+2 3X  0 X+1  1 X+2  3  1 2X+2 3X 2X+1  1  1 3X+3 3X+1 3X 3X+3 2X+3  3 2X+3  1  1  1 X+1 3X+1  3 X+1 X+1 X+3  1  1  1  1  X  1  1  1  0  1 3X+1 3X 3X+2  1
 0  0  2  0 2X  0 2X  2  2 2X+2 2X+2 2X+2  2  0 2X+2 2X+2  0  0  2 2X+2  0 2X 2X  2 2X 2X+2 2X 2X+2  0  0  2 2X  2 2X 2X 2X  2  0  2 2X+2 2X 2X+2  2 2X+2 2X  2 2X+2  0  2 2X 2X+2  0 2X+2  0  2 2X 2X+2 2X  0  2 2X 2X+2  2 2X 2X 2X 2X+2  0  2  0  2 2X  0  0 2X 2X+2  2
 0  0  0 2X 2X 2X  0 2X  0 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0 2X  0 2X  0  0 2X  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+90x^73+304x^74+236x^75+408x^76+172x^77+300x^78+128x^79+217x^80+100x^81+36x^82+36x^83+12x^84+4x^85+1x^96+2x^105+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 0.531 seconds.