The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+102x^73+125x^74+86x^75+97x^76+82x^77+114x^78+80x^79+60x^80+70x^81+71x^82+54x^83+27x^84+32x^85+9x^86+4x^87+5x^88+2x^93+1x^94+1x^96+1x^128

The gray image is a code over GF(2) with n=312, k=10 and d=146.
This code was found by Heurico 1.16 in 27.8 seconds.