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

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+334x^70+64x^71+543x^72+224x^73+760x^74+432x^75+714x^76+256x^77+338x^78+48x^79+212x^80+126x^82+33x^84+8x^86+2x^90+1x^124

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 32.9 seconds.