The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+46x^75+66x^76+112x^77+122x^78+60x^79+60x^80+4x^82+38x^83+1x^88+1x^98+1x^122

The gray image is a code over GF(2) with n=312, k=9 and d=150.
This code was found by Heurico 1.16 in 47.4 seconds.