The generator matrix

 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  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  1  1  1  1  1  1  1  1  1  X  1  1  0  1  X  1  2 X^2  1
 0  X  0  X  2  2 X+2  X X^2 X^2+X X^2 X^2+X X^2+X+2 X^2+2 X^2+X X^2+2  X  0 X^2+2 X+2 X^2+2  2  X X^2+X X^2+X X^2+X+2  0  2 X^2+X X^2 X^2 X+2 X^2  X X^2  0 X+2 X^2+X  0 X+2 X^2 X^2+X+2 X^2+X+2 X^2 X^2+X  0 X^2+2 X^2+X+2  0 X^2+X  2 X+2 X^2  X X^2+2 X^2+X+2  0 X+2 X^2+X  X X+2 X^2  0  2 X^2+2  2  0 X^2+X X^2+X X+2  2 X^2+X X^2  X X^2+2  X  0
 0  0  X  X X^2 X^2+X+2 X^2+X X^2 X^2 X^2+X+2  X X^2+2 X+2  0  2 X^2+X+2  X  0 X+2 X^2+2  2  X X^2+X+2 X^2  2 X^2+X X^2 X^2+X+2  X X^2+X+2 X^2  0  2 X+2 X+2 X^2+X  0  0  2 X^2+X+2 X^2+X+2 X+2  0 X^2+2 X^2+X+2 X^2+2  X X^2 X^2+X X^2+X X^2 X^2+2 X^2+X X^2+2 X^2  X  2 X^2+X X^2  0 X+2  X X+2 X+2 X^2+2  2 X^2+X+2  0 X^2+X  2  X X+2  X X^2+X+2  X X+2 X^2+X+2
 0  0  0  2  2  2  0  2  0  2  2  0  0  2  2  0  0  2  0  0  0  2  2  2  0  0  0  0  2  2  2  2  0  2  0  2  0  2  2  0  0  2  0  0  0  2  2  2  0  2  0  2  2  0  2  0  0  2  0  2  0  0  2  0  2  2  0  2  0  2  2  2  0  0  0  0  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+200x^73+46x^74+236x^75+282x^76+560x^77+264x^78+244x^79+34x^80+116x^81+10x^82+48x^83+2x^84+4x^85+1x^144

The gray image is a code over GF(2) with n=616, k=11 and d=292.
This code was found by Heurico 1.16 in 8.75 seconds.