The generator matrix

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

generates a code of length 74 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+344x^71+404x^72+272x^73+263x^74+250x^75+132x^76+160x^77+96x^78+50x^79+29x^80+36x^81+8x^83+1x^86+1x^96+1x^100

The gray image is a code over GF(2) with n=592, k=11 and d=284.
This code was found by Heurico 1.16 in 2.89 seconds.