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  X  1  1  2  X  2  X  X  1
 0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2  0 2X+2 2X  2  0 2X+2 2X  2  0 2X+2 2X  2  0 2X+2 2X  2 2X  2 2X  2 2X  2 2X  2  0 2X+2 2X  2  0  2 2X 2X+2 2X  2  0 2X+2 2X  2 2X  2  0 2X+2 2X  2 2X  2 2X  2  0 2X+2  0 2X+2 2X+2  0 2X+2 2X+2 2X+2 2X+2 2X+2  0  0
 0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X  0  0  0 2X  0 2X  0 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0 2X 2X  0 2X 2X  0  0
 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 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0 2X  0  0  0 2X 2X 2X  0  0 2X 2X  0 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0  0
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X  0 2X  0 2X 2X  0 2X  0  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X  0  0 2X  0  0  0 2X  0  0  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X  0 2X  0  0  0  0 2X 2X  0 2X  0 2X 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+24x^72+2x^73+42x^74+114x^75+76x^76+492x^77+75x^78+140x^79+27x^80+18x^81+10x^82+2x^83+1x^142

The gray image is a code over GF(2) with n=616, k=10 and d=288.
This code was found by Heurico 1.16 in 0.5 seconds.