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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+324x^73+347x^74+416x^75+132x^76+248x^77+231x^78+204x^79+43x^80+64x^81+12x^82+16x^83+4x^87+4x^89+1x^106+1x^110

The gray image is a code over GF(2) with n=608, k=11 and d=292.
This code was found by Heurico 1.16 in 0.328 seconds.