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  1  1  1  X  1  2  1  X  X  X
 0 2X+2  0  0  0  2 2X+2  2  0  0  0  0  2 2X+2  2 2X+2  0 2X  2 2X+2 2X 2X  2  2  2  0  2 2X+2 2X  2  0 2X  0 2X  2  2 2X+2 2X 2X  0  2 2X+2  0  0 2X 2X+2 2X+2  2 2X  2  0 2X  0  2 2X+2 2X 2X 2X+2 2X+2 2X+2  0 2X+2  0 2X  2 2X+2 2X+2 2X 2X+2 2X+2  2 2X  0 2X  0 2X+2  0
 0  0 2X+2  0  2  2 2X+2  0  2  0  0 2X+2  2 2X+2  0  0  0 2X+2 2X+2 2X  0  2  2 2X 2X+2  2 2X  0 2X 2X+2 2X+2  0 2X+2 2X 2X+2 2X  0 2X 2X+2  0  0  2 2X 2X+2  2  2 2X+2  0 2X  0 2X  2 2X  2 2X+2 2X+2  2  0  2 2X 2X  2 2X+2 2X+2  0 2X 2X 2X+2 2X  0  0 2X  0  0 2X+2 2X 2X+2
 0  0  0 2X+2  2  0 2X+2  2  2  0 2X+2  0  0 2X+2  2  0 2X  2  2  0  2 2X 2X 2X+2 2X+2  0  0  2 2X  0 2X+2  2 2X  2 2X  0  2 2X  2  2 2X 2X+2 2X 2X  2  2 2X 2X+2  0  0  2 2X+2 2X+2 2X+2  2  0  0 2X+2  0  2 2X  0  2 2X+2  0 2X  2 2X+2 2X 2X 2X+2  0 2X+2 2X+2 2X  0 2X
 0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0  0 2X  0 2X 2X 2X  0  0  0 2X  0 2X 2X 2X  0 2X 2X  0  0 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0 2X 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+164x^72+52x^74+574x^76+512x^77+488x^78+182x^80+4x^82+66x^84+4x^88+1x^144

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 0.64 seconds.