The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  1  2  1  2  0  1  1  X  0  X  X  1  X  1 X+2  1  1  X  1  1  X  0  1  0  1  1  1  1  0  2  2  1  1  X  1  0  1  1  1 X+2  0  2  1  1  1  X  X  1  2  2 X+2  0  1  0  1 X+2  1  1  1  X  2  1  1  X X+2  1  1  X  1  1
 0  1  0  0  0  2  2  2  1 X+3 X+1 X+3  1 X+1  1  X  X X+2  1  1  0 X+2  3  1  3  1  1  X  X X+3  X  1  1  2 X+2 X+3 X+1  1  1  2  1  1  0  2  1  X  X  3 X+2  X  X  1  1 X+1  1  X  1  0  0  1  1  0  1 X+1  1  1  1  3 X+2 X+2  1 X+2  X X+1 X+2  1 X+2  0  1  0  1
 0  0  1  0  2  1  3  1 X+1  1  2  3 X+1  0  0  X  X X+2 X+2 X+3  1  1 X+3  1 X+2  2  2  3  1 X+1  0  1 X+2 X+3  0  0  X  1  3  1 X+2  2 X+3  2  X X+3  1 X+3  X  0  1  1  3  2 X+1  X  0  1 X+2  0  1  1  X  3  3  X X+3  1  2 X+1 X+2  1  3 X+3  1 X+1 X+3 X+1  3  2 X+1
 0  0  0  1 X+3 X+3  0 X+1  2  0  2 X+3  1 X+1  3  1  0  3  2 X+2  2 X+3 X+1  1 X+3  3  0  X  0  X  1 X+1  X X+3  1  3  X X+2 X+3  3  1 X+2  X  X  3 X+3 X+3  0  X X+3 X+2 X+1  2 X+2 X+1 X+1  2  X  1 X+1  3 X+3  2  3 X+2  0 X+1  1 X+2  3 X+1 X+2  2 X+3  3  X X+2  X X+3  0 X+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+246x^75+286x^76+504x^77+281x^78+528x^79+304x^80+358x^81+210x^82+310x^83+208x^84+220x^85+102x^86+192x^87+50x^88+106x^89+58x^90+64x^91+14x^92+24x^93+21x^94+4x^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 1.16 in 0.972 seconds.