The generator matrix

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

generates a code of length 74 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+146x^70+172x^71+369x^72+216x^73+316x^74+224x^75+275x^76+136x^77+130x^78+20x^79+37x^80+1x^84+2x^88+3x^96

The gray image is a code over GF(2) with n=592, k=11 and d=280.
This code was found by Heurico 1.16 in 0.453 seconds.