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  1  1  1  X  X  1  1
 0 2X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 2X  0 2X  0 2X 2X 2X 2X 2X  0 2X  0 2X 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X  0 2X 2X  0
 0  0 2X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X 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  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0 2X 2X 2X  0 2X  0 2X 2X 2X  0  0 2X  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X  0 2X  0  0  0 2X  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X 2X  0 2X 2X 2X  0  0
 0  0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X 2X 2X  0 2X  0 2X  0 2X 2X 2X  0 2X 2X  0 2X 2X  0  0  0  0 2X 2X  0  0  0  0 2X 2X  0  0
 0  0  0  0  0 2X  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X 2X 2X  0 2X  0 2X 2X 2X  0 2X  0  0 2X 2X  0 2X 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0
 0  0  0  0  0  0 2X 2X  0 2X 2X  0 2X 2X 2X  0  0 2X  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X  0  0 2X  0 2X  0 2X 2X 2X  0  0 2X  0  0  0  0 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0 2X 2X 2X  0 2X 2X  0  0  0  0  0  0 2X 2X  0  0

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

Homogenous weight enumerator: w(x)=1x^0+26x^72+12x^74+32x^75+24x^76+832x^77+28x^78+32x^79+13x^80+20x^82+3x^86+1x^150

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 0.328 seconds.