The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+248x^75+308x^76+432x^77+392x^78+416x^79+291x^80+394x^81+333x^82+272x^83+153x^84+204x^85+117x^86+138x^87+87x^88+102x^89+71x^90+76x^91+23x^92+16x^93+15x^94+2x^95+1x^96+4x^97

The gray image is a code over GF(2) with n=324, k=12 and d=150.
This code was found by Heurico 1.11 in 1.51 seconds.