The generator matrix

 1  0  0  1  1  1  2  1  1  2  1  1  0  0  1  1  1  1  X X^2+X+2 X^2+X+2 X+2  1  1  1 X^2+X  1  X X^2+2  0 X^2  1 X^2  1  1  X  1  2 X+2  1  1 X^2+2  1  1  1 X+2  X  1  1  1  1  1  0  2  1 X^2 X^2+X+2  1  1  1 X^2+X+2  1 X^2+X X^2  1 X^2 X^2+X  1  1  1  1  1 X^2+X  X  1 X^2+2  1 X^2+X+2  1
 0  1  0  2 X^2+1 X^2+3  1  0 X^2+1  1  2 X^2+3  1 X^2+X X+2  X X^2+X+3 X^2+X+1 X^2+X+2 X^2+2  1  1 X+1 X^2+X+1 X^2+X  1  X  1  1  1  1  3  1 X^2+X+2  1 X^2+2  3  1  1 X+3  0 X^2+2  0  1 X+2  1  1 X^2+X+1 X+1 X+1 X^2+X  1 X+2 X^2 X+1  1  1  3 X^2+X+1 X^2+X+3  1 X^2+X  1  1 X+1  1 X^2+X+2 X^2+2 X^2+1 X^2+3 X^2+X X^2  1  1 X^2+3 X^2+X+2  3  1  0
 0  0  1 X+3 X+1  2 X^2+X+1 X^2+X X^2+1  3 X^2+3 X^2+X+2 X^2+X+2  1 X^2+X X^2+3 X+1  2  1  1 X+1  X  1  X X^2  0 X^2+X+1 X^2+X+1 X^2+3 X+2 X+3 X^2+X+2  3 X^2+X+2 X^2+X+3  1  0 X^2  1 X^2+1  3  1 X^2+2 X^2+3  1  0 X^2+3 X^2+X+2 X+1 X^2 X+1 X+3  1  1 X^2+X X^2 X^2+X+1  1 X^2+1 X^2 X^2+1 X^2+X+3  X X+1 X^2+X+3  X  1 X^2+X+1 X^2  3  3 X^2+X  1 X+3 X^2+2  1 X^2+X+3 X^2+X+3  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+162x^75+668x^76+648x^77+718x^78+468x^79+352x^80+228x^81+308x^82+146x^83+174x^84+112x^85+59x^86+24x^87+21x^88+4x^89+1x^90+1x^98+1x^102

The gray image is a code over GF(2) with n=632, k=12 and d=300.
This code was found by Heurico 1.16 in 0.375 seconds.