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  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  2  1  1  1  1  1  1  1  X  1  1  1  1  X  X
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X X^2 X^2+X  2 X+2  0 X^2+X X^2  X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2  X X^2  X  2 X^2+X+2  0 X^2+X  0 X^2+X X^2  X X^2+2 X+2 X^2+2 X+2  2 X^2+X+2  2 X^2+X+2 X^2  X X+2 X^2 X^2+2 X+2 X^2+2  X X^2  X  0  0 X^2+X  2 X^2+X  0  0 X^2+X+2 X^2+X+2 X^2+X X^2+X X^2  0  2  0 X^2+2 X^2+X X^2+X+2
 0  0 X^2+2  0 X^2 X^2  0 X^2 X^2+2  0 X^2  0  0 X^2+2  0 X^2+2  2  2  2  2 X^2 X^2 X^2+2 X^2+2  2  2  2  2 X^2 X^2 X^2+2 X^2+2  0  0 X^2+2 X^2+2 X^2 X^2+2  2  0 X^2+2 X^2 X^2 X^2  0  2  0  2 X^2+2 X^2  0  2 X^2+2  0  2 X^2  2 X^2+2  0  0 X^2+2  2 X^2  2 X^2  2 X^2 X^2+2  0 X^2 X^2 X^2+2  2 X^2+2
 0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  2  2  2  2  0  0  0  0  2  0  2  0  0  2  2  2  0  0  0  0  2  2  0  2  2  2  0  2  2  2  0  2  2  0  0  0  2  0  2  0  0  2  2  0  0  2  0  0  0  2  2  0  2  2  0  0  2  2  0
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  0  2  2  0  0  2  2  0  0  2  2  0  2  0  2  0  2  0  2  0  2  0  0  2  0  2  2  0  2  0  0  2  0  2  0  2  0  0  2  0  2  2  2  0  0  2  2  2  0  2  0  0  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+152x^70+80x^71+322x^72+352x^73+260x^74+592x^75+63x^76+120x^78+93x^80+12x^82+1x^140

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 83.2 seconds.