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

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+22x^70+32x^71+144x^72+96x^73+438x^74+96x^75+136x^76+32x^77+18x^78+6x^80+2x^82+1x^128

The gray image is a code over GF(2) with n=592, k=10 and d=280.
This code was found by Heurico 1.16 in 0.422 seconds.