The generator matrix

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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+100x^66+708x^67+1463x^68+1896x^69+3116x^70+3492x^71+4010x^72+3676x^73+4139x^74+3238x^75+2936x^76+1646x^77+1206x^78+572x^79+205x^80+176x^81+71x^82+60x^83+17x^84+14x^85+16x^86+8x^87+2x^91

The gray image is a code over GF(2) with n=584, k=15 and d=264.
This code was found by Heurico 1.16 in 11.2 seconds.