The generator matrix

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

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+116x^67+636x^68+1270x^69+2256x^70+2976x^71+3454x^72+3966x^73+4418x^74+3614x^75+3250x^76+2514x^77+1947x^78+1124x^79+564x^80+294x^81+157x^82+94x^83+68x^84+20x^85+13x^86+12x^87+3x^88+1x^90

The gray image is a code over GF(2) with n=592, k=15 and d=268.
This code was found by Heurico 1.16 in 11.4 seconds.