The generator matrix

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

generates a code of length 73 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+160x^68+252x^69+426x^70+428x^71+562x^72+592x^73+418x^74+384x^75+486x^76+244x^77+80x^78+20x^79+23x^80+2x^82+12x^84+2x^86+2x^88+2x^108

The gray image is a code over GF(2) with n=584, k=12 and d=272.
This code was found by Heurico 1.16 in 0.61 seconds.