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

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+361x^68+32x^69+494x^70+256x^71+624x^72+704x^73+544x^74+256x^75+458x^76+32x^77+218x^78+78x^80+20x^82+12x^84+4x^86+1x^88+1x^124

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 0.719 seconds.