The generator matrix

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

generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+196x^71+594x^72+698x^73+614x^74+428x^75+511x^76+280x^77+266x^78+200x^79+112x^80+78x^81+61x^82+24x^83+13x^84+16x^85+1x^86+1x^88+1x^90+1x^94

The gray image is a code over GF(2) with n=600, k=12 and d=284.
This code was found by Heurico 1.16 in 0.328 seconds.