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

generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+146x^74+750x^75+538x^76+766x^77+372x^78+458x^79+242x^80+334x^81+118x^82+136x^83+97x^84+84x^85+17x^86+32x^87+1x^88+2x^90+1x^92+1x^94

The gray image is a code over GF(2) with n=624, k=12 and d=296.
This code was found by Heurico 1.16 in 0.375 seconds.