The generator matrix

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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+114x^75+238x^76+270x^77+333x^78+260x^79+212x^80+274x^81+177x^82+104x^83+58x^84+2x^88+1x^90+2x^95+1x^110+1x^112

The gray image is a code over GF(2) with n=632, k=11 and d=300.
This code was found by Heurico 1.16 in 0.563 seconds.