The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+107x^72+404x^73+591x^74+750x^75+1000x^76+1088x^77+1196x^78+1334x^79+1313x^80+1310x^81+1231x^82+1220x^83+1149x^84+978x^85+862x^86+576x^87+446x^88+316x^89+190x^90+134x^91+71x^92+52x^93+25x^94+18x^95+9x^96+10x^97+2x^101+1x^102

The gray image is a code over GF(2) with n=324, k=14 and d=144.
This code was found by Heurico 1.16 in 15.2 seconds.