The generator matrix

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

generates a code of length 76 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+31x^70+212x^71+211x^72+534x^73+283x^74+680x^75+277x^76+686x^77+269x^78+484x^79+123x^80+178x^81+52x^82+32x^83+26x^84+10x^85+2x^86+1x^88+1x^90+1x^92+1x^94+1x^118

The gray image is a code over GF(2) with n=608, k=12 and d=280.
This code was found by Heurico 1.16 in 0.515 seconds.