The generator matrix

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

generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+94x^69+690x^70+1076x^71+1850x^72+1924x^73+2025x^74+1934x^75+1910x^76+1464x^77+1364x^78+814x^79+625x^80+266x^81+125x^82+90x^83+95x^84+10x^85+4x^86+4x^87+14x^88+2x^89+1x^92+2x^95

The gray image is a code over GF(2) with n=600, k=14 and d=276.
This code was found by Heurico 1.16 in 3.27 seconds.