The generator matrix

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

generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+256x^68+1454x^69+2938x^70+4496x^71+5229x^72+6872x^73+7460x^74+8630x^75+7616x^76+6742x^77+5393x^78+3832x^79+2208x^80+1324x^81+502x^82+378x^83+106x^84+56x^85+27x^86+4x^87+8x^88+4x^91

The gray image is a code over GF(2) with n=600, k=16 and d=272.
This code was found by Heurico 1.16 in 44.2 seconds.