The generator matrix

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

generates a code of length 74 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+280x^67+1634x^68+2810x^69+4174x^70+4920x^71+7308x^72+7574x^73+8436x^74+7722x^75+7218x^76+5024x^77+4070x^78+2106x^79+1252x^80+542x^81+268x^82+86x^83+34x^84+34x^85+20x^86+6x^87+17x^88

The gray image is a code over GF(2) with n=592, k=16 and d=268.
This code was found by Heurico 1.16 in 42.8 seconds.