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  X  X  1  X  2  0 X^2
 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  1 X^2+1 X^2+X+2  1  1  1
 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+2 X^2+X+2 X^2+2  X X^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+359x^74+324x^75+332x^76+252x^77+238x^78+180x^79+210x^80+52x^81+38x^82+24x^83+20x^84+8x^86+4x^88+4x^90+1x^98+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 3.13 seconds.