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

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+349x^72+56x^73+572x^74+192x^75+866x^76+240x^77+778x^78+256x^79+401x^80+24x^81+160x^82+128x^84+58x^86+13x^88+1x^92+1x^124

The gray image is a code over GF(2) with n=616, k=12 and d=288.
This code was found by Heurico 1.16 in 11.8 seconds.