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

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+51x^72+78x^73+231x^74+244x^75+286x^76+336x^77+361x^78+172x^79+78x^80+34x^81+111x^82+32x^83+32x^84+1x^142

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 0.719 seconds.