The generator matrix

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

generates a code of length 75 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+323x^72+360x^73+368x^74+128x^75+345x^76+224x^77+168x^78+32x^79+36x^80+24x^81+24x^82+5x^84+8x^88+2x^108

The gray image is a code over GF(2) with n=600, k=11 and d=288.
This code was found by Heurico 1.16 in 0.375 seconds.