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

generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+60x^70+96x^71+192x^72+288x^73+360x^74+224x^75+376x^76+32x^77+188x^78+64x^79+70x^80+64x^81+32x^82+1x^128

The gray image is a code over GF(2) with n=600, k=11 and d=280.
This code was found by Heurico 1.16 in 0.516 seconds.