The generator matrix

 1  0  1  1  1 X^2+X+2  1  1  0  1 X^2+X+2  1  1  1  1  2  1 X+2  1  1  0  1  1 X+2  1  1  1 X^2+X  1 X^2  1  1  1 X^2  1  1 X^2+X+2  1 X+2  X X^2  1  1  X X^2+2  1  1  1  1  1  1  1  1  1  1 X^2+2  X  1  1  1 X^2+2  1 X^2+X  1  1 X^2+X X^2+2  1  1 X^2+X+2 X^2+X  1  1  1  1
 0  1 X+1 X^2+X+2 X^2+1  1 X^2+3  0  1 X^2+X+2  1 X+1  3 X^2+X+1  2  1 X+2  1 X^2+X+3  0  1  1 X+2  1 X^2+X+3 X^2+3 X^2  1 X^2+X  1 X+1 X^2+X+2 X^2+1  1 X^2+X+3 X^2  1  3  1  1  1  X X^2+X+1 X^2  1 X^2+X+1  X  1 X^2 X^2+2 X^2+3 X^2+3 X+1  X  1  1  0 X+3 X^2+X+1 X^2+X+1  X X^2+X+1  1  0 X^2+X+2  1  1 X^2+X+2 X^2+1  1  1  2  3 X^2+2  2
 0  0 X^2  0  0  0  0 X^2 X^2+2 X^2+2 X^2 X^2+2  2 X^2 X^2+2 X^2  2  2 X^2  2  2  2 X^2 X^2+2 X^2+2 X^2  0 X^2 X^2  2  0  0 X^2+2 X^2+2  0 X^2+2  2 X^2+2 X^2+2  0  0  2  2  2 X^2  2 X^2+2 X^2  2 X^2 X^2  0  0 X^2  0  2 X^2  2 X^2+2 X^2+2  0  2 X^2+2  2 X^2+2  2 X^2  0 X^2+2 X^2  0 X^2+2  0  0  0
 0  0  0 X^2+2  2 X^2+2 X^2 X^2 X^2+2  2  0 X^2+2  0  2  0  2  2  2 X^2+2 X^2+2 X^2+2 X^2 X^2 X^2+2 X^2  0 X^2+2 X^2+2 X^2+2 X^2  2  0 X^2+2  2 X^2  2  2 X^2  2 X^2  0 X^2+2 X^2 X^2+2 X^2  0  0  2  2 X^2 X^2+2 X^2+2  0  0  2  2  2 X^2 X^2+2  2 X^2 X^2+2 X^2 X^2 X^2 X^2+2 X^2+2 X^2  0  2  2  2 X^2+2  2 X^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+70x^70+350x^71+521x^72+466x^73+501x^74+476x^75+439x^76+398x^77+376x^78+318x^79+92x^80+30x^81+23x^82+8x^83+16x^84+2x^85+2x^88+3x^90+2x^94+1x^98+1x^100

The gray image is a code over GF(2) with n=600, k=12 and d=280.
This code was found by Heurico 1.16 in 0.547 seconds.