The generator matrix

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

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+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 0.297 seconds.