The generator matrix

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

generates a code of length 77 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+178x^73+754x^74+520x^75+600x^76+560x^77+390x^78+280x^79+298x^80+178x^81+161x^82+40x^83+76x^84+28x^85+17x^86+8x^87+5x^90+1x^94+1x^96

The gray image is a code over GF(2) with n=616, k=12 and d=292.
This code was found by Heurico 1.16 in 0.344 seconds.