The generator matrix

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

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+112x^75+48x^76+88x^77+50x^78+112x^79+6x^80+48x^81+13x^82+14x^83+6x^84+8x^85+2x^88+2x^99+1x^104+1x^106

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 11.4 seconds.