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

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+38x^68+52x^70+144x^72+64x^73+584x^74+384x^75+577x^76+64x^77+24x^78+39x^80+24x^82+24x^84+20x^86+8x^88+1x^140

The gray image is a code over GF(2) with n=600, k=11 and d=272.
This code was found by Heurico 1.16 in 0.563 seconds.