The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 75.

Homogenous weight enumerator: w(x)=1x^0+104x^75+425x^76+636x^77+798x^78+1000x^79+1205x^80+1062x^81+1357x^82+1078x^83+1355x^84+1236x^85+1285x^86+1012x^87+1068x^88+764x^89+654x^90+480x^91+374x^92+188x^93+105x^94+70x^95+48x^96+26x^97+23x^98+14x^99+4x^100+4x^101+2x^102+2x^103+4x^105

The gray image is a code over GF(2) with n=336, k=14 and d=150.
This code was found by Heurico 1.16 in 15.8 seconds.