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+2  1  1 X+2  1  1  0  1  1  1  1 X^2+X  1  1  2  1  1 X^2+X+2  1  1 X^2+2  1  X  1  X  1  X  1  1  1  1  0 X+2  1  2  X  1  1  X  1 X^2+2  X  1  0  X
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  1  3 X+1  0  1 X^2+X X^2+1  1  1 X^2+2 X^2+X+3 X+2  3  1  0 X+1  1 X^2+X X^2+1  1  1 X+2 X^2+X+3  1 X^2+2  3  1  0 X+1 X^2+X X^2+1  1  2 X+3  1 X^2+X+2 X^2+3  1 X^2+2 X^2+X+3  1 X+2 X^2+2 X^2  0  0  2 X^2+2 X^2+X X+2 X^2+X+2  X  1  3  1 X^2+X  1 X^2+2 X+2 X^2+X+1  X  1  2 X^2 X^2+2
 0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  2  0  2  2  0  2  0  0  0  2  2  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  2  0  2  2  2  0  2  2  2  2  2  0  0  2  0  2  2  2  0
 0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  2  0  0  2  0  2  2  2  0  2  2  0  2  0  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  0  2  0  2
 0  0  0  0  2  0  0  2  0  0  0  2  2  2  2  2  0  2  2  2  0  2  0  2  0  2  0  0  0  0  2  2  2  2  0  2  0  2  0  0  2  2  2  0  2  2  0  0  2  0  2  2  2  2  0  0  0  0  0  2  0  2  0  2  0  0  2  0  2  2  2  0  0  2  2
 0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  2  0  0  2  2  0  0  2  0  0  2  0  2  2  0  2  0  0  2  2  0  0  0  2  2  2  0  2  2  2  0  0  2  0  0  0  0  2  0  2  2  0  2  0  0  2  0  0  2  0  2  0  0  2  2  2  0  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+252x^70+208x^71+543x^72+368x^73+535x^74+384x^75+515x^76+384x^77+439x^78+176x^79+204x^80+16x^81+37x^82+15x^84+16x^86+2x^92+1x^118

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 108 seconds.