The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  0  1  X  1 2X 2X  1
 0  X  0  X 2X 2X 3X  X  2 X+2  2 X+2 3X+2 2X+2 X+2 2X+2  X  0 2X+2 3X 2X+2 2X  X X+2 X+2 3X+2  0 2X X+2  2  2 3X  2  X  2  0 3X X+2  0 3X  2 3X+2 3X+2  2 X+2  0 2X+2 3X+2  0 X+2 2X 3X  2  X 2X+2 3X+2  0 3X X+2  X 3X  2  0 2X 2X+2 2X  0 X+2 X+2 3X 2X X+2  2  X 2X+2  X  0
 0  0  X  X  2 3X+2 X+2  2  2 3X+2  X 2X+2 3X  0 2X 3X+2  X  0 3X 2X+2 2X  X 3X+2  2 2X X+2  2 3X+2  X 3X+2  2  0 2X 3X 3X X+2  0  0 2X 3X+2 3X+2 3X  0 2X+2 3X+2 2X+2  X  2 X+2 X+2  2 2X+2 X+2 2X+2  2  X 2X X+2  2  0 3X  X 3X 3X 2X+2 2X 3X+2  0 X+2 2X  X 3X  X 3X+2  X 3X 3X+2
 0  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X  0  0 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0 2X 2X 2X  0  0  0  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+200x^73+54x^74+188x^75+402x^76+400x^77+384x^78+196x^79+42x^80+116x^81+10x^82+48x^83+2x^84+4x^85+1x^144

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 8.83 seconds.