The generator matrix

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

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+313x^74+392x^75+383x^76+148x^77+264x^78+220x^79+162x^80+32x^81+63x^82+32x^83+24x^84+4x^85+4x^88+4x^91+1x^100+1x^112

The gray image is a code over GF(2) with n=616, k=11 and d=296.
This code was found by Heurico 1.16 in 0.469 seconds.