The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+152x^74+108x^75+214x^76+52x^77+158x^78+44x^79+97x^80+8x^81+78x^82+20x^83+28x^84+4x^85+22x^86+20x^87+8x^88+4x^90+1x^96+2x^98+2x^100+1x^112

The gray image is a code over GF(2) with n=312, k=10 and d=148.
This code was found by Heurico 1.16 in 93.3 seconds.