The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+136x^74+510x^75+834x^76+1108x^77+1446x^78+1756x^79+2099x^80+2388x^81+2469x^82+2512x^83+2625x^84+2726x^85+2443x^86+2088x^87+1946x^88+1588x^89+1329x^90+1030x^91+696x^92+454x^93+243x^94+188x^95+82x^96+22x^97+30x^98+12x^99+5x^100+2x^105

The gray image is a code over GF(2) with n=336, k=15 and d=148.
This code was found by Heurico 1.13 in 21.3 seconds.