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

generates a code of length 77 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+35x^72+96x^73+50x^74+408x^75+307x^76+440x^77+300x^78+160x^79+28x^80+96x^81+33x^82+72x^83+13x^84+8x^85+1x^146

The gray image is a code over GF(2) with n=616, k=11 and d=288.
This code was found by Heurico 1.16 in 0.562 seconds.