The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+26x^72+154x^73+255x^74+246x^75+207x^76+188x^77+230x^78+166x^79+82x^80+82x^81+86x^82+74x^83+39x^84+68x^85+59x^86+40x^87+24x^88+4x^89+5x^90+4x^92+5x^94+2x^95+1x^96

The gray image is a code over GF(2) with n=312, k=11 and d=144.
This code was found by Heurico 1.11 in 0.317 seconds.