The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+2x^74+196x^75+124x^76+376x^77+124x^78+196x^79+2x^80+1x^88+1x^98+1x^122

The gray image is a code over GF(2) with n=616, k=10 and d=296.
This code was found by Heurico 1.16 in 0.312 seconds.