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  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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0 X^2+2  2  2  0 X^2+2 X^2  2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  0  0 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2 X^2+2  2  2 X^2+2 X^2  0  0 X^2 X^2+2  0 X^2  2  0 X^2 X^2+2 X^2+2  2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2  2 X^2 X^2+2 X^2 X^2 X^2+2  0  0  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2 X^2+2  0  2 X^2 X^2  2  0 X^2+2 X^2  0  0 X^2+2 X^2+2  2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2 X^2 X^2  0  2 X^2
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  0  0  0  0  0  0  2  2  2  2  0  2
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0  2  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  0  2  0  2  2

generates a code of length 77 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+69x^74+16x^75+131x^76+608x^77+114x^78+16x^79+57x^80+9x^82+2x^84+1x^148

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 62.7 seconds.