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  X  1  1  1  X  1  1  X  1  1  2  1  1 X^2  X  X
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0 X^2  0 X^2  2 X^2+2  2 X^2+2  0 X^2  2 X^2  0 X^2  2 X^2  0 X^2  2 X^2  2 X^2  2 X^2+2  0 X^2  0 X^2+2  0 X^2+2 X^2  2  2 X^2 X^2+2  0 X^2+2  0  2 X^2+2 X^2+2 X^2 X^2 X^2  2  2  2  0  2 X^2  2  0 X^2+2 X^2 X^2 X^2+2  0  0 X^2+2 X^2 X^2+2 X^2 X^2
 0  0 X^2+2 X^2  0 X^2+2 X^2  0 X^2+2  0 X^2  0  0 X^2 X^2+2  2 X^2  2  0 X^2+2  0 X^2+2 X^2+2  2  0 X^2+2 X^2  0  2 X^2 X^2+2  2  2 X^2+2 X^2+2 X^2 X^2  0  2  0 X^2  2 X^2+2 X^2+2  2  0 X^2  2 X^2  2  0 X^2+2  0  2  0  2 X^2  2 X^2 X^2+2  2 X^2+2  2  2  2 X^2+2 X^2  2 X^2+2  2 X^2+2  2  0 X^2 X^2
 0  0  0  2  0  0  2  0  0  2  0  2  2  0  2  2  2  2  2  0  0  2  2  0  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  2  2  0  2  0  2  0  0  2  0  0  0  2  0  0  2  0  0  2  2  2  2  0  0  0  2  0  0  2  2  0  2  0  0  0  0
 0  0  0  0  2  0  2  2  2  2  0  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  2  0  2  0  2  2  0  0  0  2  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  2  2  0  0  0  2  2  0  2  2  2  0  2
 0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  2  0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  0  2  2  2  0  0  2  0  0  0  2  0  2  2  0  0  2  2  2  2  0  0  2  0  0  2  0  0  2  2  2  2  2  0  2  0  0  0  2  0  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+134x^70+20x^71+69x^72+260x^73+352x^74+472x^75+282x^76+248x^77+92x^78+20x^79+23x^80+4x^81+48x^82+6x^84+14x^86+2x^88+1x^136

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 126 seconds.