The generator matrix

 1  0  0  1  1  1  0  1  2  1  1  2  1  2 X+2  1  1  1 X+2  1  2  1  X X+2  1  1  1  2  1 X+2  0  2  1  1  1  1  X  1  1  1  1  1  2 X+2  1  1  2 X+2  1  1  1  0  1  2  X  1  1 X+2  1  1  1 X+2  1  1  1  1  1  1  2  1  2 X+2  X  1  1 X+2  2  1
 0  1  0  0  1  3  1  X  1  1  2  1 X+1 X+2  1 X+3  X X+1  0 X+2  1  3  X  1  X  1  2  1 X+2  1  1  2 X+3  0  0 X+3  1 X+3  2 X+2  3  X  1  2  1  3  1  1 X+1  2 X+2  2  2  2  1 X+2  0 X+2  3  1  X  1 X+3 X+3  1 X+1 X+2  X  X X+1  0  0  1  2  0 X+2  1  0
 0  0  1 X+1 X+3  0 X+1  1  X  1  X  3  0  1  X X+2 X+1 X+3  1  X X+1  X  1 X+3  X X+3 X+1  2  2  3 X+2  1  3 X+2  3  X X+2  2 X+1 X+1 X+3  0  1  1  0 X+2 X+3  2  3 X+2 X+3  1  2  1 X+1  1  1  1 X+3  3  0  1  3  0  X X+2  X  3  0 X+2  1  1  3  X X+3  1 X+2  0
 0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  0  2  2  0  2  0  0  2  2  2  0  0  2  0  2  0  0  0  2  2  2  0  2  0  0  0  2  0  0  2  2  0  2  2  0  0  2  0  2  2  2  0  0  2  2  0
 0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  0  2  0  2  2  0  0  2  0  2  0  2  0  0  0  2  0  2  2  0  0  0  2  0  2  2  0  0  2  2  2  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  0  2  0  0  2  0  0  2  2  2  0  2  2  2  2  0  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+248x^73+164x^74+316x^75+97x^76+302x^77+71x^78+280x^79+59x^80+142x^81+56x^82+112x^83+20x^84+58x^85+14x^86+40x^87+12x^88+18x^89+12x^90+20x^91+3x^92+3x^94

The gray image is a code over GF(2) with n=312, k=11 and d=146.
This code was found by Heurico 1.16 in 63.8 seconds.